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

Answer:

the length of the rectangle is, 21 in.

Step-by-step 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.