A rectangular lawn measuring 8 m by 4 m is surrounded by a flowerbed of uniform width. The combined area of the lawn and the flowerbed is 165 m2. What is the wi

Question

A rectangular lawn measuring 8 m by 4 m is surrounded by a flowerbed of uniform width. The combined area of the lawn and the flowerbed is 165 m2. What is the width of the flowerbed? Be sure to (a) define a variable, (b) write an equation, (c) solve the equation, and (d) write a complete sentence to indicate your final solution. Do not use a system of equations.

Answer 1

the width of the flowerbed is w.

the total width is 2w+4

the total length is 2w + 8

the total area is (2w+4)(2w+8) = 165

4w^2 + 16w + 8w + 32 = 165

4w^2 + 24w + 32 = 165

4w^2 + 24w - 133 = 0

(2w - 7 )(2w + 19 ) = 0

2w + 19 = 0

w = -19/2 <-- negative measures; disqualified

2w-7 = 0

w = 7/2 = 3 and 1/2 = 3.5

Total width is 2*3.5 + 4 = 7+4 = 11

Total length is 2*3.5 + 8 = 7+8 = 15

area is 11*15 = 165

the width of the flowerbed is 3 and 1/2 = 3.5