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| Math Central | Quandaries & Queries |
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Question from Indrajit, a student: The perimeter of a triangle is equal to the perimeter of a semicircle of radius 35 cm.The ratio of the triangles is 5:6:7. Find the area of the triangle? |
Hi Indrajit.
The perimeter of the semicircle is the same as half the circumference of the circle, plus the diameter. So you will know what the perimeter of the triangle is. I'll call it P.
Knowing this, you can use Heron's Formula to relate the side lengths of the triangle to its area:
Using the semiperimeter S = P/2, Heron's Formula gives us the following for a triangle whose side ratio is 5:6:7:
Area2 = S(S-5x)(S-6x)(S-7x)
Where x is some unknown constant.
However, you also know that
P = 5x + 6x + 7x
so you can calculate x.
Cheers,
Stephen La Rocque.
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