Question

ABC is a right triangle and RS is an altitude in triangle BCR. Find the area of triangle BCR. The unit of all measurements is inches

Answer 1

ABC is a right triangle where AC and AB are the legs, and CB is the hypotenuse. Using Pythagorean theorem:

CB² = AB² + AC²

CB² = 16² + 12²

CB² = 256 + 144

CB² = 400

CB = √400

CB = 20 in

In triangle BCR, CB is the base and SR is its altitude

The area of a triangle is:

$A\text{ =}\frac{base\cdot altitude}{2}$

Then, the area of triangle BCR is:

$A=\frac{20\cdot9}{2}=90\text{ square inches}$