Question

A contractor is building a fenced-in area at a daycare. The area will be rectangular with the length of its base equal to half the length of the height. The total area will be 5000 square feet. Determine the length of fencing the contractor will use

Answer 1

The length of fencing will be
`300\ ft`

Explanation:

Step 1

Find the dimensions of the rectangle

we know that

The area of a rectangle is equal to

`A=bh`

In this problem we have

`A=5,000\ ft^(2)`

so

`5,000=bh` -----> equation A

`b=(h)/(2)` -----> equation B

Substitute equation B in equation A

`5,000=((h)/(2))h`

`10,000=h^(2)`

square root both sides

`h=100\ ft`

Find the value of b

`b=(h)/(2)` ----->
`b=(100)/(2)=50\ ft`

step 2

Find the length of fencing

The perimeter of a rectangle is equal to

`P=2(b+h)`

we have

`h=100\ ft`

`b=50\ ft`

substitute

`P=2(50+100)=300\ ft`