SOLUTION: The ratio of the areas of two triangles is 8 to 5. The altitude of one triangle is 5 centimeters more than the altitude of the other while the bases are each equal to 10 centimete

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Question 95412: The ratio of the areas of two triangles is 8 to 5. The altitude of one triangle is 5 centimeters more than the altitude of the other while the bases are each equal to 10 centimeters. Find the altitude of each triangle.

(I have tried to convert the area into an altitude so both sides will be equal, but I am not sure what to do to solve it like that.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of the areas of two triangles is 8 to 5. The altitude of one triangle is 5 centimeters more than the altitude of the other while the bases are each equal to 10 centimeters. Find the altitude of each triangle.
:
The area of triangle = .5*b*h
:
triangle 1
A1 = .5(10)h
A1 = 5h
:
Triangle 2:
A2 = .5(10)(h+5)
A2 = 5(h+5)
A2 = (5h + 25)
:
The problem tells us that: 8%2F5 = A2%2FA1
or
8%2F5 = %28%285h%2B25%29%29%2F%285h%29
:
Cross multiply:
8(5h) = 5(5h+25)
40h = 25h + 125
40h - 25h = 125
15h = 125
h = 125/15
h = 25/3 = 8.333 cm, triangle 1 altitude
:
8.333 + 5 = 13.333 cm, triangle 2 altitude
:
:
Check solutions by finding the areas:
A1 = .5*10*8.333 = 41.665
A2 = .5*10*13.333 = 66.665
:
66.665%2F41.665 = 1.6 = 8%2F5