Bob builds trailers to tow cars. He was hired to build a trailer that has an area of 96 square feet. The length of the trailer is 4 feet less than twice the width. What are the width and length of the trailer?

Question

High School

We appreciate your visit to Bob builds trailers to tow cars He was hired to build a trailer that has an area of 96 square feet The length of the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

mboluwape mboluwape · Answer 1 · 2023-10-21T23:29:32-04:00

Based on the given information, the width of the trailer is 8 feet, and the length is 12 feet.

Let's denote the width of the trailer as w (in feet).

According to the given information, the length of the trailer is 4 feet less than twice the width. We can express this as:

Length = 2w - 4

To find the area of the trailer, use the formula for the area of a rectangle: Area = Length * Width.

Substituting the values, we have:

96 = (2w - 4) * w

Expanding and rearranging the equation

2w^2 - 4w - 96 = 0

To solve this quadratic equation, factor it or use the quadratic formula. Let's use the quadratic formula:

w = (-b ± √([tex]b^2[/tex] - 4ac)) / (2a)

In this case, a = 2, b = -4, and c = -96.

Plugging in these values, we have:

w = (-(-4) ± √[tex]((-4)^2[/tex] - 4 * 2 * (-96))) / (2 * 2)

w = (4 ± √(16 + 768)) / 4

w = (4 ± √784) / 4

w = (4 ± 28) / 4

Now we have two possible solutions for the width:

w = (4 + 28) / 4 = 32 / 4 = 8 feet

w = (4 - 28) / 4 = -24 / 4 = -6 feet

Since width cannot be negative in this context, we discard the negative solution.

Therefore, the width of the trailer is 8 feet.

To find the length, substitute the width value into the expression we derived earlier:

Length = 2w - 4 = 2 * 8 - 4 = 16 - 4 = 12 feet

Therefore, the width of the trailer is 8 feet, and the length is 12 feet.

Read on width on https://brainly.com/question/15161439

#SPJ1