The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle.

Width = 7 inches, Length = 11 inches

Explanation:

Call the width of the rectangle x.

Length = x + 4

Perimeter = x + x + (x + 4) + (x + 4) = 4x + 8

Area is equal to 5 inches more than 2 times the perimeter:

Area = 5 + 2(4x + 8) = 8x + 21

The area of a rectangle also equals length times width = x(x + 4) = x² + 4x

Therefore: x² + 4x = 8x + 21

Rearrange: x² - 4x - 21 = 0

Factorize: (x - 7 )(x + 3) = 0

Therefore: x = 7, -3

Since you can't have a negative length, width is 7 inches.

(Using the first equation:)

Length is therefore = 7 + 4 = 11 inches

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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