Triangle Inequality in Real Situations

7th Grade

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| Attempts: 11 | Questions: 20 | Updated: Jan 16, 2026

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1) A right triangle must still satisfy the triangle inequality. Which of these sets of side lengths could form a right triangle?

8, 15, 17

7, 10, 25

5, 5, 12

9, 12, 25

This matches the Pythagorean triple: 8² + 15² = 64 + 225 = 289 = 17².

So it’s a valid right triangle and also obeys the triangle inequality.

Explanation

This matches the Pythagorean triple: 8² + 15² = 64 + 225 = 289 = 17².

So it’s a valid right triangle and also obeys the triangle inequality.

Submit

About This Quiz

Triangle Inequality In Real Situations - Quiz

Are you ready to see how the triangle inequality connects to real-life situations? In this quiz, you’ll solve problems about gardens, ropes, beams, and even parks to decide if certain side lengths can form a triangle. You’ll practice checking the rule with real examples, spot impossible triangles, and classify special... see moreones like isosceles and right. Step by step, you’ll discover how this simple geometry rule explains problems you might run into every day!
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2) A triangle has sides 12 m, 5 m, and x m. Which inequality describes x?

X > 17

0 < x < 5

7 < x < 17

12 < x < 17

Subtract → 12 − 5 = 7; Add → 12 + 5 = 17.

So the third side must be between 7 and 17.

Explanation

Subtract → 12 − 5 = 7; Add → 12 + 5 = 17.

So the third side must be between 7 and 17.

Submit

3) A student claims that 9, 9, and 18 form a triangle. Is this correct?

Yes, because 9 + 9 > 18

No, because 9 + 9 = 18

Yes, because 18 < 9 + 9

No, because 9 + 18 < 9

The two shorter sides equal the third. That’s a straight line, not a triangle.

The student is incorrect.

Explanation

The two shorter sides equal the third. That’s a straight line, not a triangle.

The student is incorrect.

Submit

4) A triangle has two equal sides of 10 cm. Which could be the third side?

25 cm

22 cm

20 cm

15 cm

The third side must be greater than 10 − 10 = 0 and less than 10 + 10 = 20.

15 fits that rule.

Explanation

The third side must be greater than 10 − 10 = 0 and less than 10 + 10 = 20.

15 fits that rule.

Submit

5) Which of the following sets of side lengths forms a scalene triangle?

5, 5, 5

7, 7, 10

6, 7, 8

8, 8, 12

All sides are different, and every pair adds to more than the third.

That’s a classic scalene triangle.

Explanation

All sides are different, and every pair adds to more than the third.

That’s a classic scalene triangle.

Submit

6) Maria wants to build a triangular garden with side lengths 8 ft, 12 ft, and 5 ft. Will these dimensions work?

Yes, because 8 + 5 > 12

No, because 8 + 5 = 12

Yes, because 12 + 5 < 8

No, because 8 + 12 < 5

Maria wants to build a garden in the shape of a triangle.

To check if it’s possible, we test the triangle rule:

8 + 5 = 13, which is greater than 12, so the sides can form a triangle.

✅ Maria’s plan works!

Explanation

Submit

7) A rope is cut into three pieces measuring 4 m, 9 m, and 13 m. Can these form a triangle?

Yes, because all sums are greater than the third side:

No, because 4 + 9 = 13:

No, because 9 + 13 < 4:

Yes, because 4 + 13 > 9:

Here, the rope lengths just equal the longest piece.

Since the sum of the two shorter sides must be greater than, not equal to, the third, these cannot form a triangle.

Explanation

Here, the rope lengths just equal the longest piece.

Since the sum of the two shorter sides must be greater than, not equal to, the third, these cannot form a triangle.

Submit

8) A triangle has two sides measuring 7 cm and 10 cm. Which of the following is a possible third side?

2 cm

18 cm

12 cm

20 cm

Let’s find the possible third side.

10 − 7 = 3 and 10 + 7 = 17, so the third side must be between 3 and 17.

A 12 cm side fits perfectly in that range.

Explanation

Let’s find the possible third side.

10 − 7 = 3 and 10 + 7 = 17, so the third side must be between 3 and 17.

A 12 cm side fits perfectly in that range.

Submit

9) John states 9, 12, and 20 can form a triangle. Is he correct?

Yes, because all conditions are met:

No, because 9 + 12 C 20:

Yes, because 9 + 20 > 12:

No, because 12 + 20 < 9:

John thinks these sides can make a triangle.

But 9 + 12 = 21, which is barely larger than 20.

If the sum were equal or smaller, it wouldn’t close.

This combination doesn’t safely form a triangle.

Explanation

Submit

10) A builder uses beams of lengths 6 m and 8 m for two sides of a triangular frame. Which length could be the third beam?

2 m

3 m

15 m

17 m

A builder is making a triangular frame.

The third beam must be greater than |8 − 6| = 2 and less than 8 + 6 = 14.

A 3 m beam works perfectly.

Explanation

A builder is making a triangular frame.

The third beam must be greater than |8 − 6| = 2 and less than 8 + 6 = 14.

A 3 m beam works perfectly.

Submit

11) A triangle has sides 9 cm, 14 cm, and x cm. Which inequality describes x?

5 < x < 23

0 < x < 5

9 < x < 14

X > 23

We subtract and add: 14 − 9 = 5, 14 + 9 = 23.

So x must be greater than 5 and less than 23.

Explanation

We subtract and add: 14 − 9 = 5, 14 + 9 = 23.

So x must be greater than 5 and less than 23.

Submit

12) Can a triangle have sides of 10 in, 5 in, and 16 in?

Yes, because 10 + 5 > 16

No, because 10 + 5 = 16

No, because 10 + 5 < 16

Yes, because 16 < 10 + 5

When we add the two shorter sides, 10 + 5 = 15, which is less than 16.

That means the sides would not meet – no triangle is possible.

Explanation

When we add the two shorter sides, 10 + 5 = 15, which is less than 16.

That means the sides would not meet – no triangle is possible.

Submit

13) A triangular park has two sides of 25 m and 30 m. Which of these could be the third side?

5 m

25 m

54 m

60 m

The park designer wants to find a third side.

The difference = 30 − 25 = 5, and the sum = 55.

So the third side must be between 5 and 55.

54 m fits this perfectly.

Explanation

The park designer wants to find a third side.

The difference = 30 − 25 = 5, and the sum = 55.

So the third side must be between 5 and 55.

54 m fits this perfectly.

Submit

14) A triangle has sides 13, 5, and x. Which is true?

8 < x < 18

0 < x < 8

5 < x < 13

X > 18

13 − 5 = 8 and 13 + 5 = 18, so the third side must be between 8 and 18.

Explanation

13 − 5 = 8 and 13 + 5 = 18, so the third side must be between 8 and 18.

Submit

15) A carpenter has planks of lengths 3 ft, 4 ft, and 9 ft. Can they form a triangle?

Yes, because 3 + 4 > 9

No, because 3 + 4 < 9

Yes, because 4 + 9 > 3

Yes, because 3 + 9 > 4

The carpenter cannot make a triangle because the two short planks (3 + 4 = 7) don’t reach the length of the longest plank (9).

Explanation

The carpenter cannot make a triangle because the two short planks (3 + 4 = 7) don’t reach the length of the longest plank (9).

Submit

16) Which statement about triangles is always true?

The longest side must be shorter than the shortest side.

The sum of any two sides is equal to the third side.

The sum of any two sides is less than the third side.

The sum of any two sides is greater than the third side.

This is the triangle inequality law that every triangle must follow – always!

Explanation

This is the triangle inequality law that every triangle must follow – always!

Submit

17) Which of these triples represents an impossible triangle?

3, 6, 10

7, 8, 9

5, 12, 13

9, 11, 15

Add the two shorter sides: 3 + 6 = 9, which is less than 10.

That fails the triangle rule.

Explanation

Add the two shorter sides: 3 + 6 = 9, which is less than 10.

That fails the triangle rule.

Submit

18) A triangle has sides 8 cm and 11 cm. Which of the following could be the possible length of the third side?

2 cm

4 cm

16 cm

18 cm

The third side must be greater than 11 − 8 = 3 and less than 11 + 8 = 19.

A 4 cm side fits nicely.

Explanation

The third side must be greater than 11 − 8 = 3 and less than 11 + 8 = 19.

A 4 cm side fits nicely.

Submit

19) Which set of side lengths forms an isosceles triangle?

9, 10, 11

7, 10, 12

5, 8, 13

6, 6, 9

Two sides are equal, and 6 + 6 > 9, so it forms an isosceles triangle.

Explanation

Two sides are equal, and 6 + 6 > 9, so it forms an isosceles triangle.

Submit

20) If a triangle has sides 4 cm, 7 cm, and 10 cm, which statement is true?

It is not a triangle because 4 + 7 < 10:

It is not a triangle because 4 + 10 = 7:

It is not a triangle because 7 + 10 < 4:

It is a triangle because 4 + 7 > 10:

Here, the sum of the shorter sides is 11, which is just barely enough but not strictly greater than 10.

It doesn’t satisfy the rule, so no triangle can form.

Explanation

Here, the sum of the shorter sides is 11, which is just barely enough but not strictly greater than 10.

It doesn’t satisfy the rule, so no triangle can form.

Submit