math test help needed

Question

A store is to be built on a rectangular lot that measures 70 m by 45 m. A lawn of uniform width, equal to the area of the store, must surround it. Include a diagram with your solution.

a) How wide is the strip of the lawn, to the nearest hundredth of a metre?



b) What are the length and width of the actual store?

Answer 1

Area = 70(45) = 3150 m^2

(45-2x)(70-2x) = 3150/2 = 1075

3150 -230x +4x^2 = 1075

4x^2 -230x =-1075

4(x^2-115x/2)= -1075

complete the square

x = about meters width of walk way

store's dimensions are 70-2x meters long and 45-2x meters wide

47.59m by 22,59 m

x= (45-22.59)/2=22.41/2= 11,21 meters wide walkway