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An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the area of the triangle to the area of the square? Express your answer as a common fraction.

 Jul 9, 2022
 #1
avatar+279 
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The equilateral triangle will each have side lengths of 16 and the square will have all its side lengths of 12.

The area of the square is 12^2

 

We know that the altitude of the equilateral triangle is 8sqrt(3) by the 30-60-90 we form when dividing the triangle in half. Therefore, the area of the eqilateral triangle is 64sqrt(3)

 

Therefore, the ratio will be 

 

64sqrt(3)/144, which simplifies to 4sqrt(3)/9

 Jul 9, 2022
 #2
avatar+49 
+1

here: https://web2.0calc.com/questions/perimeter_13

 Jul 9, 2022

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