Wonderful Wedge

Geometry Level pending

There is a triangular prism based on a right triangle. The length of the triangle's leg is 21 units. The hypotenuse is 4x+6 and the depth is x . If you create a rectangle using the hypotenuse and the prism's depth, the area is 1293.75 units.

(Look at image below)

What is the volume of the triangular prism?


The answer is 13041.

Isaac Mierow by Isaac Mierow , 17, USA

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2 solutions

x ( 4 x + 6 ) = 1293.75 x(4x+6)=1293.75

4 x 2 + 6 x = 1293.75 4x^2+6x=1293.75

4 x 2 + 6 x − 1293.75 4x^2+6x-1293.75

Using the quadratic formula we get x = 17.25 x=17.25

It follows that: 4 x + 6 = 4 ( 17.25 ) + 6 = 75 4x+6=4(17.25)+6=75

Using the pythagorean theorem, the length of the other leg is 7 5 2 − 2 1 2 = 72 \sqrt{75^2-21^2}=72

Solving for the volume: 1 2 × 72 × 21 × 17.25 = 13041 \dfrac{1}{2}\times 72\times21\times 17.25 = 13041 .

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Ahmad Saad
May 25, 2017

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