Question

A rectanglar field has a length that is 150 feet less than three times the width. If the area of the feiod is 70,200 square feet what is the length of the field?
A. 465 feet. B. 390 feet. C. 153 feet
D. 180 feet

Answer 1

The answer is b.

The length of the rectangle is 3w-150.
The width is w.

To get area you multiply length and width so w(3w-150)=70,200. The numbers in parentheses is the length.
You use distributive property and distribute the w to get 3w^2-150w=70,200.
You can simplify the equation by dividing both sides by 3 to get w^2-50w=23,400.
Then you get all the numbers on the left side of the equation by subtracting 23,400 to get w^2-50w-23,400=0.
Now that the equation equals zero, you can factor it to get (w+130)(w-180)=0.
Then you find the values for x with each factor which are x=-130 or x=180.
We would use the positive value for x because it is area.
You substitute 180 for x in 3w-150 and you would get 390.