Q:

The length of a rectangular deck is 4 times its width.If the deck perimeter is 30 feet, what is the deck’s area?

Accepted Solution

A:
The area of the deck is 36 square feet.Solution:Assume l is the length of the deck; w is its width, P is its perimeter and A is its area.Given that length of a rectangular deck is 4 times its width[tex]\Rightarrow l=4w \rightarrow(1)[/tex]Perimeter of the deck is 30 ft[tex]\text{Perimeter of a rectangle} = 2(\text{ length }+\text{ width })\rightarrow(2)[/tex]On substituting all the given values in (2) we get,[tex]\Rightarrow30=2(4w+w) \rightarrow \frac{30}{2}=5w \rightarrow 15=5w[/tex]On dividing we get,[tex]\Rightarrow w=\frac{15}{5} \rightarrow w=3 ft[/tex]If w=3, [tex]\rightarrow l=4\times 3=12 ft[/tex][tex]\text { Area }=\text{ width } \times \text{ length }[/tex]On substituting the values in the above formula we get,[tex]A=12\times3=36 \text{ square feet }[/tex]