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