Answer:
Option (A)
Step-by-step explanation:
Option (A).
Since, perimeter of a square = 4×(side)
Perimeters of 3 squares = 12 ft, 16 ft and 20 ft
Side lengths of three squares will be = [tex]\frac{12}{4}, \frac{16}{4},\frac{20}{4}[/tex]
= 3 ft, 4 ft and 5 ft
If these sides are the measures of the sides of the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
5² = 4² + 3²
25 = 16 + 9
25 = 25
True.
Therefore, these are the sides of the given right triangle.
Option (B).
Perimeters of three squares are 20 ft, 16 ft and 24 ft.
Sides lengths of three squares = [tex]\frac{20}{4},\frac{16}{4}, \frac{24}{4}[/tex]
= 5 ft, 4 ft and 6 ft
By Pythagoras theorem,
6² = 4² + 5²
36 = 61
False.
Therefore, these sides are not of the given right triangle.
Option (C)
Perimeters of the squares = 40 ft, 80 ft and 120 ft
Side lengths of the squares = 10 ft, 20 ft and 30 ft
If these sides are the sides of the given right triangle, they will follow the Pythagoras theorem.
By Pythagoras theorem,
(30)² = (10)² + (20)²
900 = 500
False.
Option (D)
Perimeters of the given squares are 16 ft, 24 ft and 28 ft.
Side lengths of these squares will be 4 ft, 6 ft and 7 ft.
If these sides form a right triangle they will follow the Pythagoras theorem.
By Pythagoras theorem,
7² = 4² + 6²
49 = 16 + 36
49 = 52
False.
Therefore, these are not the sides of a right triangle.
Option (A) will be the answer.
