Question

A rectangle has a width that is twice the length. If the area of the rectangle is represented by the expression 18x² + 48x + 32, what expression represents the length of the rectangle? Explain.

Answer 1

Explanation:

Length of rectangle = l (let length of rectangle be 'l')

Width of rectangle = 2l

Area of rectangle = lb --> l(2l)

∴ Here, the area is given =
`18x^2 + 48x + 32`

So,

Area of rectangle = lb

`18x^2 + 48x + 32` = l x 2l

`18x^2 + 48x + 32` =
`2l^2`

`(18x^2 + 48x + 32)/(2)` =
`l^2`

`\sqrt{(18x^2 + 48x + 32)/(2)}` =
`l`

∴ Length is
`\sqrt{(18x^2 + 48x + 32)/(2)}`