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| Math Central | Quandaries & Queries |
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Question from Brian: how can I find the base of an isosceles triangle from the height and the perimeter? |
Hi Brian,
Suppose the base has length b, each of the other two sides has length a, the perimeter is p and the height is h. Let Q be the midpoint of the base and draw a line from Q to the apex of the triangle P.
By the symmetry angle PQR is a right angle and thus the Theorem of Pythagoras applies so that
a2 = h2 + (b/2)2.
You also know that
2a + b = p.
Use these equations to find an expression for b in terms of p and h.
Penny
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