A rectangular banner is 5 inches longer than its width. A triangular poster is 3 times as long as its height. Both the poster and the banner has an area of 24 square inches.

Part A: What is the height and base of the poster? Justify your answer.

Part B: What is the length and width of the banner? Justify your answer.

Part A

For the triangle

A = (B*h) / 2 A=24

B=3*h

A = (3*h) * h/2 = (3*h^2) / 2=24

3*h^2=48 h^2=16 h=4 B = 3*4 B=12

the height and base of the poster are h=4 and B=12 respectively

Part B

For the rectangle

Area A=L*W

L=5+W A=L*W=24 A=L*W = (5+W) * W = 5*W+W^2 5*W+W^2=24 W^2+5*W-24=0 (W-3) * (W+8) = 0

Only positive W values make sense here

(W-3) = 0 W=3 L = 5+W L = 5+3 L=8

the length and width of the banner are W = 3 and L=8 respectively.