Question

He length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 317in squared .in2. find the lengths of the sides of the two squares

Answer 1

Let the length of smaller square is = x in.

So the length of longer square is = (x+3)

Area of smaller square = $x^2$ inch^2

Area of larger square is = $(x+3)^2$ inch^2

So sum of area of both square is 317.

$x^2 + (x+3)^2 = 317$

$x^2 + x^2 + 6x + 9 = 317$

$2x^2 + 6x - 308 = 0$

We can write it as

$x^2 + 3x - 154 = 0$

$x^2 + 14x - 11x - 154 = 0$

$x(x+14) - 11(x+14) = 0$

$(x+14)(x-11) = 0$

So x = 11 because we will neglect negative number.

So the length of smaller square is = 11 inch.

Length of larger side = 14 inch.