Algebra/Math What is the width?

Question

A rectangular lawn measuring 8 m by 4 m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165 m^2. What is the width of the flower bed?

Answer 1

Make a drawing!

Area = length * width

L=8+2x and W = 4+2x

LW = 165 = (8+2x)(4+2x) = 32 + 24x + 4x²

4x² + 24x - 133 = 0

The quadratic formula gives an extraneous root and x = 3.5

Length = 15 and Width = 11