Question

The area of a square is `w^2+14w+49` square inches. How do you find the length of each side of the square?

Answer 1

`w+7` inches

Explanation:

to find the area of a square, you square the length of one side.

this means that the side length of a square is the square root of its area.

if the area of a square is `w^2+14w+49`, then the side length will be the square root of `w^2+14w+49`.

to find this, it is a good idea to first factorise the expression `w^2+14w+49`.

to do this, you should find two numbers that add to make `14` and multiply to make `49`.

those two numbers here are the same number: `7` and `7`.

`7+7 = 14`
`7 * 7 = 49`

this means that the expression can be factorised to `(w+7)(w+7)`.

if you multiply out the brackets for `(w+7)(w+7)` using FOIL, you get `w^2+7w+7w+49`, which is `w^2+14w+49`.

since `w+7` and `w+7` are the same expression, `(w+7)(w+7)` can be written as `(w+7)^2`.

therefore `(w+7)^2 = w^2+14w+49`, which means that the square root of `w^2+14w+49` is `w+7`.

if the area of the square is `w^2+14w+49` square inches, then the side length is `w+7` inches.