Question

the length of the top of a rectangular desk is 24inches more than the width. What are the dimensions of the desk if the area of the top is 1,620 square inches?

Answer 1

The dimensions of the desk are

Length: 54 inches

Width: 30 inches

Explanation:

we know that

The area of rectangle is equal to

`A=LW`

where

L is the length

W is the width

we have

`A=1,620\ in^2`

so

`1,620=LW` ----> equation A

`L=W+24` ----> equation B

substitute equation B in equation A

`1,620=(W+24)W`

solve for W

`1,620=W^2+24W`

`W^2+24W-1,620=0`

Solve the quadratic equation by graphing

The solution is W=30 in

see the attached figure

Find the value of L

`L=30+24=54\ in`

therefore

The dimensions of the desk are

Length: 54 inches

Width: 30 inches