Question

A rectangle has a width of 2.5. When the length of this rectangle is decreased by 5 inches, the new area of the rectangle is 17.5.
Part A: Write an equation to represent this situation, where x represents the original length of the rectangle.
Part B: Find the original length of the rectangle.

Answer 1

Part A: An equation to represent this situation, where x represents the original length of the rectangle is:

$17.5 = (x-5) \times 2.5$

Part B: Original length of the rectangle is 12 inches

Solution:

Given that,

A rectangle has a width of 2.5

Therefore,

width = 2.5 inches

Let "x" be the original length of the rectangle

When the length of this rectangle is decreased by 5 inches

Therefore,

New length = x - 5

The new area of the rectangle is 17.5 square inches

Therefore,

The area of rectangle is given as:

$Area = length \times width$

$17.5 = (x-5) \times 2.5\\\\17.5 = 2.5x - 12.5\\\\2.5x = 17.5 + 12.5\\\\2.5x = 30\\\\x = 12$

Thus original length of the rectangle is 12 inches

Answer 2

We will find that the answers are:

• a) 17.5 in^2 = (L - 5 in)*2.5 in
• b) L = 12in

Working with rectangles.

We know that for a rectangle of length L and width W the area is given as:

A = L*W

Here we know that the width is:

W = 2.5

a) If we decrease the length by 5 inches we have:

L' = (L - 5 inches).

In this case, we get that the area is:

17.5 in^2 = (L - 5 in)*2.5 in

b) Now we can solve that to get the value of L.

(17.5 in^2)/(2.5 in) = L - 5 in

7 in = L - 5in

7in + 5in = L = 12in

So the length of the rectangle measures 12 inches.

If you want to learn more about rectangles, you can read:

https://brainly.com/question/17297081