Question

The Area Of a square is Equal to the Area of a Rectangle whose measures are 16cm and 9cm.Find the Perimeter of the square. Also find the ratio of the lengths of the diagonal of the Square and the rectangle.

Answer 1

area of square =area of rectangle
let x be the side of square
x^2=9×16
x=root9×16
x=12cm
perimeter of square =4×12
=48
diagonal of square =root 2x^2
=67.88
diagonal of rectangle=root l^2+b^2
=18.3
diagonal of square: diagonal of rectangle=67.8/18.3

Answer 2

Firstly we will have to find the area of rectangle which will be equal to length x breadth...
so the area would be 16x9= 144cmsq
Now we can find the sides of the square using the formula of area of square which is (side)^2
..suppose X is side of the square therefore
(X)^2=144
therefore X=√144
therefore X=12
Now we can find the perimeter of square by using the perimeter formula of square that is 4(side)
so there perimeter of the square will be 4X= 12x4= 48cm
Now to find the ratio of diagonals of square and rectangle ..first we will have to find the length of the diagonals which we can find easily using Pythagoras theorem
so according to Pythagoras theorem the diagonal of rectangle will be = 18.35cm
and the diagonal of square will be 17cm
so the ratio will be 18.45:17 that will be equal to 1.07