Answer:
Length of rectangle = 12 inches
Width of rectangle = 6 inches
Step-by-step explanation:
Let the width of rectangle in inches be = [tex]w[/tex]
Given: The length of rectangle is 6 inches longer than its width.
So, length of rectangle in inches [tex]l=w+6[/tex]
Perimeter of a rectangle is = [tex]2(l+w)[/tex]
Plugging in [tex]l=w+6[/tex] in the perimeter formula.
Perimeter of rectangle in terms of width = [tex]2(w+6+w)[/tex]
Simplifying and using distribution.
⇒ [tex]2(2w+6)[/tex]
⇒ [tex](2\times 2w)+(2\times6)[/tex]
⇒ [tex]4w+12[/tex]
We are given perimeter of rectangle = 36 inches.
So, we can equate to find [tex]w[/tex]
[tex]4w+12=36[/tex]
Subtracting both sides by 12.
[tex]4w+12-12=36-12[/tex]
[tex]4w=24[/tex]
Dividing both sides by 4.
[tex]\frac{4w}{4}=\frac{24}{4}[/tex]
[tex]w=6[/tex] inches
Using [tex]w=6[/tex] to find [tex]l[/tex]
[tex]l=6+6=12[/tex] inches
Length of rectangle = 12 inches
Width of rectangle = 6 inches
