Question

A rectangle is drawn so that the width is 4 feet shorter than the length. The area of the rectangle is 45 square feet. Find the length of the rectangle.

Answer 1

The length of the rectangle is 9 feet

Step-by-step explanation:

A rectangle is drawn so that:

• The width is 4 feet shorter than the length
• The area of the rectangle is 45 square feet

Assume that the length of the rectangle is x feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle is 4 feet shorter than the length

∴ The width of the rectangle = (x - 4) feet

∵ The area of the rectangle = length × width

∴ The area of the rectangle = x(x - 4)

- Simplify it

∴ The area of the rectangle = x² - 4x

∵ The area of the square = 45 feet²

- Equate the two expressions of the area

∴ x² - 4x = 45

- Subtract 45 from both sides

∴ x² - 4x - 45 = 0

Use your calculator to find the value of x

∴ x = 9 and x = -5

- We will reject the value of x = -5 because there is no negative

  dimensions

∴ x = 9

∵ The length of the rectangle = x

∴ The length of the rectangle = 9 feet

The length of the rectangle is 9 feet

Learn more:

You can learn more about area of figures in brainly.com/question/4713715

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