Question

The length of a rectangle is three more than twice the width. Determine the dimensions that give a total area of 27ft squared What are the length and width?

Answer 1

The length of a rectangle is three more than twice the width. Determine the dimensions that give a total area of 27ft squared



What are the length and width?​

Remember that

the area of a rectangle is

A=L*W

we have

A=27 ft2

so

27=L*W ------> equation 1

and

L=2W+3 ----> equation 2

substitute equation 2 in equation 1

27=(2W+3)*W

solve for W

27=2w^2+3w

2w^2+3w-27=0

solve the quadratic equation using the formula

a=2

b=3

c=-27

substitute

`w=\frac{-3\pm\sqrt[]{3^2-4(2)(-27)}}{2(2)}`
`\begin{gathered} w=\frac{-3\pm\sqrt[]{225}}{4} \\ w=(-3\pm15)/(4) \\ \end{gathered}`

therefore

W=3 and W=-18/4 (is not solution)

For W=3 ft

Fiind the value of L

L=2W+3

L=2(3)+3=9 ft

therefore

answer is

length is 9 ft and width is 3 ft