A factory is to be built on a lot measuring 270 ft by 360 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory.

Question

What must the width of the lawn be? ___________

If the dimensions of the factory are A ft by B ft with A < B, then A = ________ and B = ___________

required to show work mathematically.

Answer 1

Draw and label a diagram!!

w represents the width of the lawn

(270 + 2w)(360 + 2w) = 2(270)(360)

Can you solve for w and answer?

Answer 2

270 by 360 = 97,200 ft^2

(270+x)(360+x) =2(97200)

solve for x

97200 + 1260x + x^2 = 194400

x^2 + 1260x -97200 = 0

x^2 + 1260x + 630^2 = 97200+ 630^2

(x+630)^2 = 494100

x= -630 + 10sqr4941

x = about 703 -630 = about 73 feet

divide by 2

36.5 ft