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

To find the lengths of the sides of the two squares, set up a system of equations. Solve for the side length of the smaller square and then find the side length of the larger square. The lengths of the sides of the squares are 8 inches and 11 inches.

Step-by-step explanation:

To find the lengths of the sides of the two squares, we can start by setting up a system of equations. Let's represent the length of the side of the smaller square as 'x'.

The larger square has sides that are 3 inches longer, so its side length can be represented as 'x+3'.

The sum of the areas of the squares is given as 317 square inches. The area of a square is calculated by squaring its side length, so we have the equation x^2 + (x+3)^2 = 317.

Simplifying this equation, we get x^2 + x^2 + 6x + 9 = 317. Combining like terms, we have 2x^2 + 6x + 9 = 317.

Subtracting 317 from both sides, we get 2x^2 + 6x - 308 = 0.

Now we can solve this quadratic equation. We can factor it or use the quadratic formula. After solving, we find that the possible values for x are -19 and 8. We discard the negative value since the length cannot be negative.

Therefore, the lengths of the sides of the smaller and larger squares are 8 inches and 11 inches, respectively.

Answer 2

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.