Question

The perimeter of a rectangle is equal to twice the sum of its length and its width. One rectangle has a length of 13 1/8 inches and a perimeter of 42 1/2 inches. Write an equation that can be used to find the width of the rectangle. Explain how you found your answer.

Answer 1

8 1/8 inches

Explanation:

P = 2 ( l+w)

l = 13 1/8

P = 42 1/2

Substitute the two values into the equation

42 1/2 = 2 ( 13 1/8 + w)

Change the mixed numbers to improper fractions

42 1/2 = ( 2 *42+1)/2 = 85/2

13 1/8 = ( 8*13+1) /8 =105/8

85/2= 2 (105/8+ w)

Divide each side by 2

85/2 *1/2= 2/2 (105/8+ w)

85/4 = (105/8+ w)

Subtract 105/8 from each side

85/4 -105/8 = (105/8-105/8+ w)

Get a common denominator

170/8 -105/8 = w

65/8 = w

Change back to a mixed number

64/8 + 1/8 = w

8 1/8