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.
