Question

The length of a rectangular deck is 4 times its width.

If the deck perimeter is 30 feet, what is the deck’s area?

Answer 1

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

`\Rightarrow l=4w \rightarrow(1)`

Perimeter of the deck is 30 ft

`\text{Perimeter of a rectangle} = 2(\text{ length }+\text{ width })\rightarrow(2)`

On substituting all the given values in (2) we get,

`\Rightarrow30=2(4w+w) \rightarrow (30)/(2)=5w \rightarrow 15=5w`

On dividing we get,

`\Rightarrow w=(15)/(5) \rightarrow w=3 ft`

If w=3,
`\rightarrow l=4* 3=12 ft`

`\text { Area }=\text{ width } * \text{ length }`

On substituting the values in the above formula we get,

`A=12*3=36 \text{ square feet }`