Question

The width of a rectangle is 9 in. shorter than its length. The area of the rectangle is 252 in². What is the length of the rectangle? Enter your answer in the box. in

Answer 1

The length of the rectangle is 21 in.

Explanation:

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Answer 2

the length of the rectangle is, 21 in.

Explanation:

Area of the rectangle(A) is given by:

`A=lw` .....[1]

where,

l is the length of the rectangle

w is the width of the rectangle.

As per the statement:

The width of a rectangle is 9 in. shorter than its length.

⇒
`w = l-9`

It is also given that:

The area of the rectangle is 252 in².

⇒A = 252 in².

Substitute in [1] we have;

`252 = l(l-9)`

⇒
`252 = l^2-9l`

⇒
`l^2-9l -252 = 0`

Factorize this equation:

Split the middle term;

⇒
`l^2-21l+12l-252=0`

⇒
`l(l-21)+12(l-21)=0`

⇒
`(l-21)(l+12)=0`

By zero product property we have;

`l-21 =0` and
`l+12 =0`

⇒
`l = 21` and
`l = -12`

Since, length cannot be in negative

⇒
`l = 21 in.`

Therefore, the length of the rectangle is, 21 inches.