We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB is parallel to DE. If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

Guest Dec 16, 2020

#1**+2 **

We have triangle ABC where AB = AC and AD is an altitude. Meanwhile, E is a point on AC such that AB is parallel to DE. If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

[ABDE] = 3/4[ABC]

Guest Dec 16, 2020

#2**+1 **

Area ABC = (1/2) BC * AD

200 = (1/2) 15 * AD

400 = 15 * AD

400 / 15 = AD

80/3 = AD

See the following image :

Since AB is parallel to DE.....triangle EDC is similar to triangle ABC

And DC and BC are corresponding sides

Sinc AB = AC....then AD bisects BC...so

DC =(1/2) BC

So the scale factor of EDC to ABC = 1/2

So the area of EDC to ABC = (scale factor)^2 (area of ABC ) = (1/4) (200) = 50 = [EDC ]

So [ ABDE ] = [ ABC ] - [EDC ] = 200 - 50 = 150

CPhill Dec 16, 2020