Difference between revisions of "1994 AJHSME Problems/Problem 16"
Mrdavid445 (talk | contribs) (Created page with "==Problem== The perimeter of one square is <math>3</math> times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?...") |
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<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 9</math> | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 9</math> | ||
| + | |||
| + | ==Solution== | ||
| + | Let <math>a</math> be the sidelength of one square, and <math>b</math> be the sidelength of the other, where <math>a>b</math>. If the perimeter of one is <math>3</math> times the other's, then <math>a=3b</math>. The area of the larger square over the area of the smaller square is | ||
| + | |||
| + | <cmath>\frac{a^2}{b^2} = \frac{(3b)^2}{b^2} = \frac{9b^2}{b^2} = \boxed{\text{(E)}\ 9}</cmath> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1994|num-b=15|num-a=17}} | ||
Revision as of 00:55, 23 December 2012
Problem
The perimeter of one square is 
times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
Solution
Let 
be the sidelength of one square, and 
be the sidelength of the other, where 
. If the perimeter of one is times the other's, then 
. The area of the larger square over the area of the smaller square is
![\[\frac{a^2}{b^2} = \frac{(3b)^2}{b^2} = \frac{9b^2}{b^2} = \boxed{\text{(E)}\ 9}\]](http://latex.artofproblemsolving.com/c/b/c/cbc115bbf734e16f47e5441bce602c4c4398f029.png)
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
