An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $56$ and the triangle has an area of $112$ . What are the lengths of sides A and B?

Question

1505 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-12T00:08:30

$20 sqrt{2}$

Let's renotate and say triangle ABC has $a=b$ , $c=56$ area $A=112$ .

Archimedes' Theorem is a modern version of Heron's Formula,

$16A^2 = 4 a^2 c^2 - (b^2 - a^2 - c^2)$

$16(112)^2 = 4a^2 (56)^2 - 56^4$

$a = 20 sqrt{2}$

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 56 56 and the triangle has an area of 112 112 . What are the lengths of sides A and B?