A rectangle has a length of 16 inches less than 8 times its width. If the area of the rectangle is 5824 square inches, find the length of the rectangle.

Question

A rectangle has a length of 1616 inches less than 88 times its width. If the area of the rectangle is 58245824 square inches, find the length of the rectangle.



Answer 1

The first sentence is easiest if you read it BACKWARDS in short phrases.

Its width W

8 times its width. 8W

16 less than 8 times its width. 8W - 16

So the length is 8W - 16. and the width is W

The area is length and width multiplied together.

So. W ( 8W - 16) = 5824

Expand 8W² - 16W = 5824

Set to 0. 8W² - 16W - 5824 = 0

Divide by 8 W² - 2W - 728 = 0

Factor. (W - 28)(W + 26) = 0

Set each to 0. W - 28 = 0 W + 26 = 0

Solve each W = 28 W = -26

Discard the negative answer.

Solve for Length L = 8 ( 28) - 16

L = 208

Check your answer by multiplying length X width.

208 x 28 = 5824.

YEAH!!

Do you need help finding the factors?