Question

A photograph is in the shape of a rectangle. It has a Iength of (x + 2) inches and a width of (x -2) inches. What is the area of the photograph?

Answer 1

The area of the photograph is:
`A=x^2-4`

Explanation:

Given

The length of rectangular photograph =
`l` = (x + 2) inches

The width of rectangular photograph =
`w` = (x - 2) inches

To determine

The area of the photograph

Important Tip:

Given that the photograph is in the shape of a rectangle. Thus, we can use the formula involving the area of a rectangle to determine the area of a photograph.

The Area of the photograph can be determined using the formula

`A = wl`

where

• 
  `A` is the area

• 
  `l` is the length

• 
  `w` is the width

now substituting
`l = (x + 2)` and
`w = (x-2)` in the formula

`A = wl`

`A = (x-2) (x+2)`

Apply Difference of Two Squares Formula:
`\left(a-b\right)\left(a+b\right)=a^2-b^2`

`A=x^2-2^2` ∵
`a=x,\:b=2`

`A=x^2-4` ∵
`2^2=4`

Therefore, the area of the photograph is:
`A=x^2-4`