SOLUTION: How do I find the height of a triangle if I am only given the length of 2 sides? Problem: In ΔABC, AB = 24 cm and BC = 15 cm. CD bisects AB. ΔCDB is a right triangl

Question 523965: How do I find the height of a triangle if I am only given the length of 2 sides?
Problem:
In ΔABC, AB = 24 cm and BC = 15 cm.
CD bisects AB.
ΔCDB is a right triangle.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You are given a lot more than just the measure of two sides, though I have to simply assume that point D is on the segment

(you didn't specifically say so and you didn't provide a diagram). With that presumption, knowing that

bisects

and that

is right, then CD is a perpendicular bisector of AB. That means that

is congruent to

(by SAS) and ABC is an isosceles triangle with C as the apex and AB as the base. Further, you know that

. From that you can see that

is a right triangle with a leg that measures 12 and a hypotenuse that measures 15. You can either use Pythagoras or recognize a 3-4-5 proportion right triangle to determine that the short leg, specifically

, measures 9. From that you calculate the area by base times height divided by 2.

John

My calculator said it, I believe it, that settles it

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SOLUTION: How do I find the height of a triangle if I am only given the length of 2 sides? Problem: In &#916;ABC, AB = 24 cm and BC = 15 cm. CD bisects AB. &#916;CDB is a right triangl

SOLUTION: How do I find the height of a triangle if I am only given the length of 2 sides? Problem: In ΔABC, AB = 24 cm and BC = 15 cm. CD bisects AB. ΔCDB is a right triangl