Question

"find the perimeter and diagonal of a square whose area is equal to the area of a rectangle whose lengthis 9m and breadth is 4m."

Answer 1

let the side o of square = x
a/q,
       area of square = area of recangle
or,   $x^{2}$ = 9×4
or,  x = $\sqrt{36}$
therefore, x=6 m
we know that , perimeter of square = 4×x
perimeter of square = 4×6 =24 m
now, diagonal of square = $\sqrt{ x^{2}+ x^{2} }$
   or, diagonal of square = $\sqrt{2 x^{2} }$
   or, diagonal of square = $\sqrt{2}$×x
   or, diagonal of square = 6$\sqrt{2}$ m = 8.52 m

Answer 2

given,
Area of rectangle = Area of square
Area of rectangle = length × breadth
                         = 9 × 4
                         = 36m²
therefore,area of square = 36m²
w.k.t.Area of square = (side)²
                              = 36 = 6²
        side = 6m
let the side be 'a'
        a = 6
Perimeter of square = 4a
                              = 4×6 = 24m
Diagonal of the square = √2 a
                                 = 6√2m