Question

sum ot the area of two squares is 468m. if the different of their perimeters is 24m. find the sides of two squares.

Answer 1

Area of square = Side length squared

Perimeter of square = Side length x 4

Let X be the side of the bigger square, and Y be the side of the smaller square

This means X^2 + Y^2 = 468 and 4X - 4Y = 24

Divide 4X - 4Y = 24 on both sides to get X - Y = 6

Square both sides of X - Y = 6 to get X^2 + Y^2 - 2XY = 36

Subtract the equations to get 2XY =  432 or XY = 216

The only factors that fit this is 12 x 18: 12 x 18 = 216 and 18 - 12 is 6

So, X is 18 and Y is 12.