Question

The right triangle above has height h centimeters and hypotenuse t centimeters. What is the area, in square centimeters, of the triangle, in terms of h and t ?

Answer 1

Answer:

$A = \frac{h\sqrt{t^{2} - h^{2}}}{2}$

Step-by-step explanation:

Right triangle:

height h, width w, hypotenuse h

Area is: $A = \frac{h*w}{2}$

Pytagoras theorem: $h^{2} + w^{2} = t^{2}$

In this question:

To find the area, in terms of h and t, we have to write w as a function of h and t. So

$h^{2} + w^{2} = t^{2}$

$w^{2} = t^{2} - h^{2}$

$w = \sqrt{t^{2} - h^{2}}$

So the area is:

$A = \frac{h*w}{2}$

$A = \frac{h\sqrt{t^{2} - h^{2}}}{2}$