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?

Question

10314 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-30T09:28:32

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#