SOLUTION: in a triangle a base and the cooesponding height are in the ratio 3:2. The area is 108 in. squared. find the base and the corresponding height.

Question 133639: in a triangle a base and the cooesponding height are in the ratio 3:2. The area is 108 in. squared. find the base and the corresponding height.
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
The area of triangle is found by using the formula:
A = 1/2 times base times height
The ratio 3:2 becomes 3x:2x
We need to find x BEFORE we can find the length of the base and height in terms of inches.
The area is 108.
We now plug and chug.
108 = 1/2 (3x)(2x)
108 = 1/2(6x^2)
108 = 3x^2
Divide both sides by 3.
108/3 = x^2
36 = x^2
Take square root of both sides.
+ -6 = x
Of course, when dealing with base and height, we are talking about distance.
Distance CANNOT be negative. So, we REJECT the answer x = -6.
We use x = 6.
Base is 3x.
Base = 3(6)
Base = 18 inches
================
Height is 2x.
Height = 2(6)
Height = 12 inches.
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