Question

m∠B=90 in ΔABC. BM is altitude to AC.If BM=2√ 30, MC=6, find AC.

Answer 1

According to Geometric Mean Theorem.

If h denotes the altitude in a right triangle and p and q the segments on the hypotenuse then the theorem can be stated as:

{\displaystyle h={\sqrt {pq}}} h={\sqrt {pq}}

Here, h = BM=2√30

Answer 2

BM=√AC

squaring on both the sides

(2√30)²=AM+MC

4×30=AM+6

120/6=AM

AM=20

AC=AM+MC

AC=20+6

AC=26