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?

Height ##=12 cm##

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.

##Areatriangle = 1/2 * 18*10## ## = 90cm^2##

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

So the area equation for the second triangle ##=1/2*15*x##

Since the areas are equal,

##90 = 1/2 * 15*x##

Times both sides by 2.

##180 = 15x## ##x=12##

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