SOLUTION: 1. The perimeter of a rectangular banner is 72 inches. The width of the banner is 1/3 it's length. What is the area of the banner? 2. The perimeter of a rectangular patio is 80 fe

Algebra ->  Rectangles -> SOLUTION: 1. The perimeter of a rectangular banner is 72 inches. The width of the banner is 1/3 it's length. What is the area of the banner? 2. The perimeter of a rectangular patio is 80 fe      Log On


   

Question 1010622: 1. The perimeter of a rectangular banner is 72 inches. The width of the banner is 1/3 it's length. What is the area of the banner?
2. The perimeter of a rectangular patio is 80 feet. The width of the patio is 2/3 its length. What is the area of the patio?
3. The perimeter of a rectangular table is 132 inches. The length of the table is 1 3/4 times its width. What is the area of the table?
4. The perimeter of a rectangular poster is 84 inches. The length of the poster is 2 1/2 times its width. What is the area of the poster?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The four questions are all very much alike, except for the material of the rectangular piece and the values.

Dimensions x and y.
Perimeter p is known.
x and y are related by some known factor, k.
y=kx, and either variable might be taken as width or length, depending on how the described specific problem is arranged.
Question asks for area, the value of xy.

KNOWN: p, k
UNKNOWN: x, y

Each of the four problems goes this way.
system%28p=2x%2B2y%2Cy=kx%29

p=2x%2B2%28kx%29
%282%2B2k%29x=p
highlight%28x=p%2F%282%2B2k%29%29

Use x to solve for y.
y=kx
y=k%28p%2F%282%2B2k%29%29
highlight%28y=kp%2F%282%2B2k%29%29



Finally, each of the questions asks for area, xy.
highlight_green%28%28kp%5E2%29%2F%282%2B2k%29%5E2%29
which you might want as
highlight%28%28kp%5E2%29%2F%284%281%2Bk%29%5E2%29%29