SOLUTION: A triangle has a side length of 3 inches and an area of 22 square inches. A similar triangle has a corresponding side length of 6 sinches. Find the area of the larger triangle.

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Question 1078749: A triangle has a side length of 3 inches and an area of 22 square inches. A similar triangle has a corresponding side length of 6 sinches. Find the area of the larger triangle.
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
When the side is doubled, the area increases 4 fold; 88 in^2.
The suppose the side is the base. The height is 14 2/3, because (1/2)3*44/3=22
Now make that side 6. The height is doubled as well (similar triangles) to 29 1/3
(1/2)*6*(88/3)=88

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

A triangle has a side length of 3 inches and an area of 22 square inches. A similar triangle has a corresponding side length of 6 sinches. Find the area of the larger triangle.
The ratio of the corresponding sides of 2 similar TRIANGLES is equal to the square root of the ratio of their areas.

Ratio of one of smaller triangle's sides to corresponding side of larger triangle: 3%2F6

Let the area of the larger triangle be A

With the area of the smaller triangle being 22 sq inches, we get: 3%2F6+=+sqrt%2822%29%2Fsqrt%28A%29

1%2F2+=+sqrt%2822%29%2Fsqrt%28A%29 ------- Reducing 3%2F6

1%5E2%2F2%5E2+=+%28sqrt%2822%29%5E2%29%2F%28sqrt%28A%29%5E2%29 ------- Squaring both sides 

1%2F4+=+22%2FA

Cross-multiplying, we get the area of larger triangle, or: