Question

What is the length of each side of a square when the given area is m^2 + 10m + 25? And what is the perimeter?

Answer 1

See a solution process below:

Explanation:

The formula for the area of a square is:

`A = s^2` where `s` is the length of the side of the square.

Because we know the area is `m^2 + 10m + 25` we can substitute this for `A` and solve for `s` to find the length of the sides of the square.

`m^2 + 10m + 25 = s^2`

`(m + 5)^2 = s^2`

`sqrt((m + 5)^2) = sqrt(s^2)`

`m + 5 = s`

`s = m + 5`

The length of each side of the square is: `m + 5`

The formula for the perimeter of a square is:

`p = 4s`

We can substitute `(m + 5)` for `s` to find the perimeter of this square:

`p = 4(m + 5)`

Or

`p = (4 xx m) + (4 xx 5)`

`p = 4m + 20`

Answer 2

Length of each side: `(m+5)`
Perimeter: `4(m+5)`

Explanation:

You are given a quadratic equation: `m^2 +10m+ 25`
Simplifying it gives:
`m^2+5m+5m+25`
then: `m(m+5) +5(m+5)`
so its area = `(m+5)(m+5)` which means each side is equal to `(m+5)`
so its perimeter is `4(m+5)`

Answer 3

see a solution process below;

Explanation:

Note the following formulas;

`"Area of a square" = l^2`

`"Perimeter of a square" = 4l`

Where;

`l = "length of each sides of the square"`

We have the area of the square to be;

`l^2 = m^2 + 10m + 25 = 0`

Which is a quadratic equation, hence we solve for the values of `m`

`m^2 + 10m + 25`, factors are; `+5 and +5`

`m^2 + 5m + 5m + 25`

`(m^2 + 5m) (+ 5m + 25)`

`m(m + 5) +5(m + 5)`

`(m + 5) (m + 5)`

Now we have broken down the equation, proceed further..

`l^2 = m^2 + 10m + 25 = 0`

`l^2 = (m + 5) (m + 5)`

`l^2 = (m + 5)^2`

`l = m + 5`

Hence, the length of each sides of the square are `m + 5`

Therefore, we now find the perimeter of the square..

Note;

`"Perimeter of a square" = 4l`

`p = 4(m + 5)`

Hence, the perimeter of the square is `4(m + 5)`