contestada

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.

Respuesta :

calculista

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.