Question

Monica is building a model of a soccer field that she is proposing being built by Hartford High School. In her model, the length is a certain number of inches and the width is 12 inches less than the length. The total area of the model is 45 square inches. What are the dimensions of the model?

FAST PLEASE

Answer 1

Length: 15 inches

Width: 3 inches

Explanation:

Let'

L ----> the length of the model in inches

W ---> the width of the model in inches

we know that

The area of the model is given by the formula

`A=LW`

we have

`A=45\ in^2`

so

`45=LW` ----> equation A

Remember that

the width is 12 inches less than the length

so

`W=L-12` ---> equation B

substitute equation B in equation A

`45=L(L-12)`

solve for L

`45=L^2-12L`

`L^2-12L-45=0`

Solve the quadratic equation by graphing

using a graphing tool

The solution is L=15 in

see the attached figure

Find the value of W

`W=L-12`

substitute the value of L

`W=15-12=3\ in`

therefore

The dimensions of the model are

Length: 15 inches

Width: 3 inches