Which of the following has the greatest perimeter?
A. A square with an area of 36 square units. B. An equilateral triangle with a side of 9 units. C. A rectangle with 10 units length and 40 square units area. D. A right triangle whose one side is 4 units and hypotenuse 5 units. E. All the given figures have the same perimeter.
A rectangle with 10 units length and 40 square units area. -option a is not correct.
area of the square = 36 square units = s2 or s = 6 units.
perimeter of the square= 4s = 4 6 units = 24 units.
option b is not correct.
side of the equilateral triangle = a = 9 units.
perimeter of an equilateral triangle = 3a = 3 9 units = 27 units.
option c is correct.
length of the rectangle = 10 units.
area of the rectangle = 40 square units.
width of the rectangle = 40/10 units = 4 units.
perimeter of the rectangle = 2(l + w)
= 2(10 + 4) units
= 2 14 = 28 units.
option d is not correct.
in a right triangle c2= a2 + b2 or 52 = 42 + b2 or b2 = 25 - 16 or b2 = 9
or b = 3. perimeter of the triangle = (3 + 4 + 5) units = 12 units.
option e is not correct as is observed no two of the given figures have the same perimeter.