SOLUTION: Topic: Similarities (I don't know if proofs is the right section) Trapezoid ABCD has base lengths AB=30 and CD = 54... https://media.discordapp.net/attachments/8027514148745379

Algebra ->  Geometry-proofs -> SOLUTION: Topic: Similarities (I don't know if proofs is the right section) Trapezoid ABCD has base lengths AB=30 and CD = 54... https://media.discordapp.net/attachments/8027514148745379      Log On


   

Question 1177021: Topic: Similarities (I don't know if proofs is the right section)
Trapezoid ABCD has base lengths AB=30 and CD = 54...
https://media.discordapp.net/attachments/802751414874537995/821169436152299591/Yc9JivxDYHQ5ERgAAiRCBmCQLesiabQsQ0kFEQEiQAQGkABJkQEcdOoyESACRMAyAiRFLENJBREBIkAEBpAASZEBHHTqMhEgAkTA.png
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Congruent diagonals means the trapezoid is isosceles, and triangles ABX and CDX are both isosceles.

The bases of triangles ABX and CDX are 30 and 54, so the ratio of similarity between the two triangles is 30:54 = 5:9.

That means the ratio of corresponding sides AX and CX is 5:9.

And since the length of AC is 56, that makes AX=20 and CX=36.

Triangle ABC is then isosceles with legs 20 and base 30.

A perpendicular from X to side AB divides triangle ABC into two congruent right triangles with hypotenuse 20 and one leg 30/2=15.

Use the Pythagorean Theorem to find the height of triangle ABC; then use that height and the base to find the area of the triangle using area = one-half base times height.