# The base of a triangle of a given area varies inversely as the height. A triangle has a base of 18cm and a height of 10cm. How do you find the height of a triangle of equal area and with base 15cm?

Oct 30, 2015

Height $= 12 c m$

#### Explanation:

The area of a triangle can be determined with the equation  area = 1/2 * base * height

Find the area of the first triangle, by substituting the measurements of the triangle into the equation.

$A r e a \triangle = \frac{1}{2} \cdot 18 \cdot 10$
$= 90 c {m}^{2}$

Let the height of the second triangle $= x$.

So the area equation for the second triangle $= \frac{1}{2} \cdot 15 \cdot x$

Since the areas are equal,

$90 = \frac{1}{2} \cdot 15 \cdot x$

Times both sides by 2.

$180 = 15 x$
$x = 12$