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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the area of a triangle is Area+=+%28base%2Aheight%29%2F2
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 24+in%5E2.
Now we can plug these values in for area, base, and height in our equation: 24+=+%283h%2Ah%29%2F2
3h*h simplifies to 3h%5E2: 24+=+3h%5E2%2F2
Multiply both sides of the equation by 2: 48+=+3h%5E2
Divide both sides of the equation by 3: 16+=+h%5E2
Square root both sides of the equation: sqrt%2816%29+=+sqrt%28h%5E2%29
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.