Given the information w=4 inches and h=7 inches, find two ways to evaluate 2w+2h. What is the geometric significance of this calculation?

Question

Given the information w=4 inches and h=7 inches, find two ways to evaluate 2w+2h. What is the geometric significance of this calculation?

 

Answer 1

It is the perimeter of a rectangular wall of width w and height h.

 

(1) Evaluate 2w + 2h = 2(w + h) = 2(4 + 7) inches = 22 inches

 

(2) Let A = wh = area of wall = 4*7 = 28 inches squared

 

Then 2w + 2h = 2(A/h) + 2(A/w) = 2(28/7) + 2(28/4) = 22 inches

 

(There just are not too many ways to rearrange 2w + 2h)