The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length?

Question

Tequila

Mathematics

8 November, 20:23

The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length?

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Hull · Answer 1

1. Given that the width of the rectangle is x, and the area of the rectangle may be represented by the equation x^2 + 5x = 300, we can solve this equation for the width (x) as such:

x^2 + 5x = 300

x^2 + 5x - 300 = 0 (Subtract 300 from both sides)

(x - 15) (x + 20) = 0 (Factorise x^2 + 5x - 300)

From this, we get: x = 15 or x = - 20

Since the width must be a positive length (ie. more than 0), - 20 would be an invalid answer in the given context and thus the width is given by x = 15.

2. If we know that the length is 5 inches more than the width, we simply need to add 5 to the width we found above to obtain the length:

Length = x + 5

Length = 15 + 5 = 20

Thus, the width of the rectangle is 15 inches and the length of the rectangle is 20 inches.