In triangle and . Point on divides it into segments of length and . What is the length of segment ?

Source: NCTM Mathematics Teacher 2006

**SOLUTION**

**
**Using the Heron’s area formula to calculate the area of triangle

Area = where

Area =

is the altitude of triangle

Area =

Using the Pythagorean theorem in right triangle

Using the Pythagorean theorem in right triangle

**Answer**:

*Alternative solution*

*
*Using the law of cosines in triangle

Using the law of cosines in triangle

Multiply Eq. by and add Eq.

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