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


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
Altitude \overline{BD} in an isosceles triangle is also a perpendicular bisector.
BC^2=BD^2+DC^2 by the Pythagorean theorem
Perimeter of triangle ABC

Answer: 18 length units


About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s