Answer:
the length of the rectangle is, 21 in.
Step-by-step explanation:
Area of the rectangle(A) is given by:
[tex]A=lw[/tex] .....[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.
⇒[tex]w = l-9[/tex]
It is also given that:
The area of the rectangle is 252 in².
⇒A = 252 in².
Substitute in [1] we have;
[tex]252 = l(l-9)[/tex]
⇒[tex]252 = l^2-9l[/tex]
⇒[tex]l^2-9l -252 = 0[/tex]
Factorize this equation:
Split the middle term;
⇒[tex]l^2-21l+12l-252=0[/tex]
⇒[tex]l(l-21)+12(l-21)=0[/tex]
⇒[tex](l-21)(l+12)=0[/tex]
By zero product property we have;
[tex]l-21 =0[/tex] and [tex]l+12 =0[/tex]
⇒[tex]l = 21[/tex] and [tex]l = -12[/tex]
Since, length cannot be in negative
⇒[tex]l = 21 in.[/tex]
Therefore, the length of the rectangle is, 21 inches.
Answer:
The length of the rectangle is 21 in.
Step-by-step explanation:
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