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Difference between revisions of "1962 AHSME Problems/Problem 6"

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==Solution==
 
==Solution==
  
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To solve for the perimeter of the triangle we plug in the formula for the area of an equilateral triangle which is (x^2*<math>\sqrt{3}</math>)/4. This has to be equal to <math>9 \sqrt{3}</math> so solving for x brings the answer to a side length to 6. Knowing this gives us a perimeter of 18 so each side length of the square is 4.5. Now we solve for the diagonal getting the answer of D, <math>{9\sqrt{2}}/{2}</math>.
+
To solve for the perimeter of the triangle we plug in the formula for the area of an equilateral triangle which is (x^2*<math>\sqrt{3}</math>)/4. This has to be equal to <math>9 \sqrt{3}</math> so solving for x brings the answer to a side length to 6. Knowing this gives us a perimeter of 18 so each side length of the square is 4.5. Now we solve for the diagonal getting the answer of <math>\boxed{D}</math> <math>{9\sqrt{2}}/{2}</math>.
  
 
==See Also==
 
==See Also==

Revision as of 12:19, 12 February 2018

Problem

A square and an equilateral triangle have equal perimeters. The area of the triangle is $9 \sqrt{3}$ square inches. Expressed in inches the diagonal of the square is:

$\textbf{(A)}\ \frac{9}{2}\qquad\textbf{(B)}\ 2\sqrt{5}\qquad\textbf{(C)}\ 4\sqrt{2}\qquad\textbf{(D)}\ \frac{9\sqrt{2}}{2}\qquad\textbf{(E)}\ \text{none of these}$

Solution

To solve for the perimeter of the triangle we plug in the formula for the area of an equilateral triangle which is (x^2*$\sqrt{3}$)/4. This has to be equal to $9 \sqrt{3}$ so solving for x brings the answer to a side length to 6. Knowing this gives us a perimeter of 18 so each side length of the square is 4.5. Now we solve for the diagonal getting the answer of $\boxed{D}$ ${9\sqrt{2}}/{2}$.

See Also

1962 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 5 		Followed by
Problem 7
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40
All AHSME Problems and Solutions

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