Question

The area of the rectangle is 35cm squared if the bottom and top of the rectangle are x+2 and the left and right side equals x, what is the expression of rectangle in terms of x?

Answer 1

`x=5color(white)(.)cm`

Explanation:

Area is width times length.

Let width (shortest) be `w=x`
Let the length be `L=x+2`

Area`->wL=35 cm^2`

Drop the units of measurement for now

`x xx (x+2) = 35`

`x^2+2x=35`

Subtract 35 from both sides

`x^2+2x-35=0`

Notice that `5xx7=35 and 7-5=2`

Factorising

`(x-5)(x+7)=0" " =>" " x=5 and -7`

The -7 is not a logical solution for this question so ignore it

`x=5color(white)(.)cm`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
`w=x=5`
`L=x+2=7`

Area `=5xx7=35` as expected