Isosceles Triangle

Isosceles triangle ABC has a base of length 8 units. \overline{BD} is the altitude to the base, and E is the midpoint of side \overline{BC}. The triangular area BDE is three square units. Find the perimeter of triangle ABC.

Source: NCTM Mathematics Teacher 2008

SOLUTION

Let F be the midpoint of \overline{AB}. Triangle FBE is an isosceles triangle and its area is one fourth the area of triangle ABC because its area equals the area of triangle BDE.
Area of ABC=4 times area of BDE
\dfrac{1}{2}AC\cdot BD=4\cdot 3
\dfrac{1}{2}8\cdot BD=12
BD=3
Altitude \overline{BD} in an isosceles triangle is also a perpendicular bisector.
BC^2=BD^2+DC^2 by the Pythagorean theorem
=3^2+4^2
=25
BC=5
Perimeter of triangle ABC
8+5+5=18

Answer: 18 length units

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About mvtrinh

Retired high school math teacher.
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