# 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. Find the height of a triangle of equal area and with base 15cm

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. Find the height of a triangle of equal area and with base 15cm
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

The area of a triangle can be determined with the equation $area=\frac{1}{2}\cdot base\cdot height$
Find the area of the first triangle, by substituting the measurements of the triangle into the equation.
$Area△=\frac{1}{2}\cdot 18\cdot 10$
$=90c{m}^{2}$
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=15x
x=12