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

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Answer 1 · 2018-04-02T10:46:59

$w+7$ inches

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.

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