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The length of a particular rectangle is 2 inches less than twice its width. If the area of the rectangle is 40 square inches, find the length and width.

Question 1 options:


length is 6 in, width is 4 in


length is 5 in, width is 8 in


length is 2 in, width is 2 in


length is 8 in, width is 5 in

Verified Answer :

ROBERT567

length is 8
width is 5

facundo3141592

By solving a system of equations, we will see that the correct option is:

"length is 8 in, width is 5 in"

How to find the system of equations?

First, we know that for a rectangle of width W and length L the area is given by:

A = LW

Here we know that:

L = 2W - 2in

A = 40 in^2 = LW

That is or system of equations, to solve it, we replace the first equation into the second one.

40 in^2 = (2W - 2in)W

40 in^2 = 2W^2 - 2inW

2W^2 - 2inW - 40 in^2 = 0

This is a quadratic equation, the solutions are given by the Bhaskara's formula:

\(W = \frac{(2in) \pm \sqrt{(-2in)^2 - 4*2*(-40in)} }{2*2} \\\\W = \frac{(2in) \pm 18in }{4}\\\)

We only care for the positive solution, so we have:

W = (2in + 18in)/4 = 5in

Then:

L = 2W - 2in = 25in  - 2in = 8in

The correct option is:

"length is 8 in, width is 5 in"

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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