## Saturday, April 20, 2013

### More Triangle Problems

Category: Plane Geometry, Algebra

"Published in Suisun City, California, USA"

A right triangle has an area of 54 in2. The product of the lengths of the three sides is 1620 in3. What are the lengths of its sides?

Solution:

To illustrate the problem, it is better to draw the figure as follows Photo by Math Principles in Everyday Life

We know that the area of a right triangle is

If the product of the sides of a triangle is 1620 in3, then we can solve for the length of hypotenuse as follows

Use Pythagorean Theorem in order to solve for the other sides of a right triangle as follows

To solve for a and b, we need to use another equation which is

or

Substitute the value of b to the above equation, we have

Multiply both sides of the equation by a2, we have

Use Quadratic Formula in order to solve for a2 as follows

If we choose the positive sign,

The other side of a right triangle is

If we choose the negative sign,

The other side of a right triangle is

Therefore, the three sides of a right triangle are 9, 12, and 15