SOLUTION: two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle

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Question 951261: two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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similar triangles have proportional corresponding sides, proportional perimeters, and proportional areas
if two similar triangles have perimeters of P%5B1%5D=10 and P%5B2%5D=30, then
P%5B1%5D%2FP%5B2%5D=10%2F30
P%5B1%5D%2FP%5B2%5D=1%2F3
or ratio of similarity is 1%2F3
the smaller triangle has an area of A%5B1%5D=4 square what is the area of the larger triangle A%5B2%5D
ratio_+of+_areas=%28ratio+_of+_similarity%29%5E2
ratio_+of+_areas=%281%2F3%29%5E2
ratio_+of+_areas=1%2F9
so, A%5B1%5D%2F+A%5B2%5D=1%2F9
4%2F+A%5B2%5D=1%2F9
4%2A9=A%5B2%5D
A%5B2%5D=36

Answer by josgarithmetic(39620) About Me  (Show Source):
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If right-triangles,

b and h,
%281%2F2%29bh=4 and b%2Bh%2Bsqrt%28b%5E2%2Bh%5E2%29=10


The bigger triangle,
each length is some factor k times larger than for the small triangle,
%281%2F2%29%28b%2Ak%29%28h%2Ak%29 and bk%2Bhk%2Bsqrt%28b%5E2%2Ak%5E2%2Bh%5E2%2Ak%5E2%29=30;
-
system%28%281%2F2%29bh%2Ak%5E2=B%2C+bk%2Bhk%2Bk%2Asqrt%28b%5E2%2Bh%5E2%29=30%29

system%284%2Ak%5E2=B%2Ck%28b%2Bh%2Bsqrt%28b%5E2%2Bh%5E2%29%29=30%29

system%284%2Ak%5E2=B%2Ck%2810%29=30%29

The perimeter or second equation tells that k=3; and then the first or area equation tells that B=4%2A3%5E2=4%2A9=highlight%2836%29.

Answer by MathTherapy(10552) About Me  (Show Source):
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two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle
Since the similar triangles’ perimeters are in a 10%3A30, or 1%3A3 ratio, their sides will be in a 1%3A3, or 1%2F3 ratio also.



If the sides of similar triangles are in a certain ratio, then their areas will be in the SQUARE of their sides' ratio. 

Thus, areas of smaller and larger triangles will be in the ratio of 1%5E2%2F3%5E2, or 1%2F9

Let area of larger triangle, be A

Then we get: 1%2F9+=+4%2FA

1(A) = 9(4) --------- Cross-multiplying 

A, or area of larger triangle = highlight_green%2836%29 sq inches