SOLUTION: the area of a triangle varies jointly as the base and the height.A triangle with a base of 8cm and a height of a 9cm has an area of 36 square centimeters.find the are when the base

Question 1144038: the area of a triangle varies jointly as the base and the height.A triangle with a base of 8cm and a height of a 9cm has an area of 36 square centimeters.find the are when the base is 10cm and height is7cm?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
joint variation formula is z = k * x * y
in your problem, z = 36 = thee area of the triangle and x = 8 = the base of the triangle and y = 9 = the height of the triangle.
the formula becomes 36 = k * 8 * 9 which becomes 36 = k * 72
solve for k to get k = 36/72 = 1/2
the formula becomes 36 = 1/2 * 8 * 9 which becomes 36 = 36, confirming the value of k is equal to 1/2.
when the base is 10 and the height is 7, the formula becomes z = 1/2 * 10 * 7 which becomes z = 35.
that's the area of the triangle and that's your solution.
instead of z = k * x * y, we could have said a = k * b * h
a would be the area
b would be the base
h would be the height.
with k = 1/2, you would then get a = 1/2 * b * h
this is the formula for the area of a triangle that you might be familiar with.

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