Find the perimeter and diagonal of a square whose area is equal to the area of a rectangle with a length of 9 m and a breadth of 4 m.
Answer (2)
A re a o f a rec t an g l e : A = 9 m × 4 m = 36 m 2 a − s i d e o f a s q u a re A re a o f a s q u a re : A = a 2 A = A ⇒ a 2 = 36 m 2 ⇒ a = 36 m 2 ⇒ a = 6 m P er im e t er o f t h e s q u a re : P = 4 a ⇒ P = 4 × 6 m = 24 m D ia g o na l o f t h e s q u a re : d = a 2 ⇒ d = 6 2 m
The perimeter of the square is 24 m, and the diagonal is 6√2 m. These measurements are derived by equating the square's area to that of a rectangle measuring 9 m by 4 m. The side length of the square is 6 m.
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