In ∆abc, ab=20 cm, ac=15 cm. the length of altitude an is 12 cm. prove that ∆abc is a right triangle. show your work.

Remark

Technically you can't. You are not sure how ABC are arranged. I'm taking it that the "right angle" is at A.  If you have a diagram that tells you that is the wrong assumption, please leave a note.

Step One

Find the area of the triangle

Area = 1/2* AB * AE

Area = 1/2*20*15

Area = 150 cm^2

Step Two

Using the area from step one and the altitude find the "hypotenuse."

Area = hypotenuse * altitude/2

Area = 150

hypotenuse = ?

altitude = 12

150 = 1/2 * h * 12

150 = 6*h

h = 25

Step three

Does this produce a right triangle triple? check

a = 15

b = 20

c = 25

a^2 + b^2 = c^2

15^2 + 20^2 = 25^2

225 + 400= 625

625 = 625 It checks and therefore the triangle is a right triangle.