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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

Respuesta :

Let the length of smaller square is = x in.

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

Area of smaller square = [tex]x^2[/tex] inch^2

Area of larger square is = [tex](x+3)^2[/tex] inch^2

So sum of area of both square is 317.

[tex]x^2 + (x+3)^2 = 317[/tex]

[tex]x^2 + x^2 + 6x + 9 = 317[/tex]

[tex]2x^2 + 6x - 308 = 0[/tex]

We can write it as

[tex]x^2 + 3x - 154 = 0[/tex]

[tex]x^2 + 14x - 11x - 154 = 0[/tex]

[tex]x(x+14) - 11(x+14) = 0[/tex]

[tex](x+14)(x-11) = 0[/tex]

So x = 11 because we will neglect negative number.

So the length of smaller square is = 11 inch.

Length of larger side = 14 inch.

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