Question

A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.

A. Find the original perimeter and area of the garden

B. Find the perimeter and area of the garden with a 20% increase in each dimension.

C. By what percent will the perimeter increase? By what percent will the area increase?

D. Explain why the area and perimeter will not increase by the same percentage.

Answer 1

w=12 ft

l= 20 ft

A.

P= 2(12+20)= 64 ft

A= 12*20= 240 ft²

B.

P=2(12*1.2+20*1.2)= 76.8 ft

A= 12*1.2*20*1.2= 345.6 ft²

C.

(76.8-64)/64*100%= 20%

(345.6- 240)/240*100%= 44%

D.

perimeter increase is linear function of one dimension increase

area increase is function of 2 dimensions increase