Question

What is number 8 please

Answer 1

12

Explanation:

Let's use x to describe the length of a side of the square.

Let's use a to describe the area of the square.

Let's use p to describe the perimeter of the square.

The area of a square is the length of its side to the power of two: a=x²

The perimeter of a square is the sum of its four sides: p=x+x+x+x or p=4x

We're told that the are here is 96 more than the perimeter: a=p+96

Let's sub x² in for a, and 4x in for p:

a=p+96

x²=4x+96

x²-4x-96=0

This is a quadratic equation in the form x²+mx+n=0, which can be simplified to the form (x+h)(x+g)=0, where h+g=m and hg=n. Find h and g by finding a mulitple pair of n that, when added/subtracted from one another, give m.

x²-4x-96=0

(x+8)(x-12)=0

The only was to get zero through multiplication is if one of the terms you're multiplying by is zero. So either x+8=0 or x-12=0.

If x+8=0, x=-8

If x-12=0, x=12

So x = -8 or 12, but the side length cannot be a minus number so we rule out -8, leaving us with out final answer: 12

Answer 2

`\textsf{ the length of the side }\sf= \boxed{\sf 12}`

Explanation:

Let the side of the square be s. The area of the square is s² and the perimeter is 4s.

Note:

`\sf \textsf{Area of square} = Length * Length= Length^2`

`\sf \textsf{Perimeter of square}= 4 * length`

We are given that the area is numerically 96 more than the perimeter.

This means that:

`\sf s^2 = 4s + 96`

We can solve for s by rearranging the equation:

`\sf s^2 - 4s - 96 = 0`

We can factor the left side of the equation by middle term factorization:

`\sf s^2 -(12-8) s - 96 = 0`

Distribute the bracket:

`\sf s^2 - 12s+8s - 96 = 0`

Take common from each two terms:

`\sf s(s-12)+8(s-12)`

Take common again and keep remaining in bracket:

(s - 12)(s + 8) = 0

Either

s = 12

or

S = - 8

Therefore,

`\sf s = 12\textsf{ or }s = -8`

Since the side of a square cannot be negative.

So,

`\textsf{ the length of the side }\sf= \boxed{\sf 12}`