SOLUTION: a rectangle has a perimeter of 14 inches.A similar rectangle has a perimeter of 42 inches.The area of smaller rectangle is 10 square inches.What is the area of the larger rectangl

Algebra ->  Rectangles -> SOLUTION: a rectangle has a perimeter of 14 inches.A similar rectangle has a perimeter of 42 inches.The area of smaller rectangle is 10 square inches.What is the area of the larger rectangl      Log On


   

Question 874164: a rectangle has a perimeter of 14 inches.A similar rectangle has a perimeter of 42 inches.The area of smaller rectangle is 10 square inches.What is the area of the larger rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2x+2y=14 and 6x+6y=42, and xy=10.
This seems like we only need one, the smaller rectangle, and its area; until later....

x+y=7 and xy=10.
y=7-x;
x%287-x%29=10
-x%5E2%2B7x-10=0
x%5E2-7x%2B10=0
%28x-2%29%28x-5%29=0
The dimensions are 2 and 5 for the smaller rectangle.

The proportionality for similarity, 42%2F14, is found to be 3, linearly, so the larger rectangle dimensions are 2%2A3=6 and 5%2A3=15
Meaning the area of the larger rectangle is highlight%286%2A15=90%29