How wide is the walkway?

Question

A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walk way of uniform width around it. The area of the new garden is one-half the area of the old garden.

Answer 1

(30-2w)(40-2w)=(1/2)(30)(40)

1200-80w-60w+4w^2=600

4w^2-140w+1200-600=0

4w^2-140w+600=0

w^2-35w+150=0

150=2*3*5*5=30*5 and 30+5=35

factor

(w-30)(w-5)=0

w-30=0

w=30 (don't use this number because you will get negative dimensions)

w-5=0

w=5 feet is the width of the walkway

(30-10)(40-10)=20*30=600 which is half of 30*40 which is 1200