SOLUTION: The length of the base of a triangle is three times the height. The area of the triangle is 24 in2. Find the length of the base of the triangle
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Question 565137: The length of the base of a triangle is three times the height. The area of the triangle is 24 in2. Find the length of the base of the triangle
Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
The formula for the area of a triangle is
Let us call the height of the triangle h. Since the base of the triangle is three times the height, we can call the base 3h. As you said, the area is .
Now we can plug these values in for area, base, and height in our equation:
3h*h simplifies to :
Multiply both sides of the equation by 2:
Divide both sides of the equation by 3:
Square root both sides of the equation:
Simplify: 4 = h
As a result, the height of the triangle is 4. However, the question is asking for the base, not the height, so we need to plug the value for h into the expression for the base: 3h = 3(4) = 12
Therefore, the length of the base is 12 inches.
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