Isosceles triangle has a base of length units. is the altitude to the base, and is the midpoint of side . The triangular area is three square units. Find the perimeter of triangle .

Source: NCTM Mathematics Teacher 2008

**SOLUTION**

**
**Let be the midpoint of . Triangle is an isosceles triangle and its area is one fourth the area of triangle because its area equals the area of triangle .

Area of times area of

Altitude in an isosceles triangle is also a perpendicular bisector.

by the Pythagorean theorem

Perimeter of triangle

**Answer**: length units

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