A rectangular brochure is designed so that it has an area of 19.5 square inches and a perimeter of 19 inches. Find the width and height of the brochure. Assume the height is greater than the width.

Question

A rectangular brochure is designed so that it has an area of 19.5 square inches and a perimeter of 19 inches. Find the width and height of the brochure. Assume the height is greater than the width. 

Answer 1

2(W+H) = 19

W+H = 19/2 = 9.5

wH=19.5

H=19.5/W

W + 19.5/W = 9.5

W^2 + 19.5 = 9.5W

W^2 -9.5W +19.5 = 0

W = 9.5/2 - (1/2)sqr(9.5^2 - 4(19.5))

= 4.75 - .5(90.25 - 78) = 4.75 -.5(sqr12.25) = 4.75 - 3.5/2 = 4.75-1.75 = 3 in.

H=19.5/3 = 6.5 in.

height = 6 1/2 inches

width = 3 inches

3x6.5 = 19.5

2(3+6.5) =2(9.5 = 19