In a triangle the ratio of the base to its altitude is 2:3. If the area of the trianlge is 108 square units, what is the length of the base?
Let x = base, then 3/2x = altitude.
Area = 1/2 b * h
108 = 1/2x * 3/2x
Solve for x.
Thank you!!!
To solve this problem, we can use the formula for the area of a triangle:
Area = (1/2) * base * altitude.
Let's call the length of the base "x" and the length of the altitude "y".
We are given that the ratio of the base to its altitude is 2:3, which means x/y = 2/3.
We also know that the area of the triangle is 108 square units.
Using the formula for the area, we can substitute the given values: 108 = (1/2) * x * y.
Now, we can substitute the ratio x/y = 2/3 into the equation:
108 = (1/2) * (2/3) * y * y.
Simplifying this equation, we have:
108 = (1/3) * y^2.
Multiply both sides of the equation by 3 to eliminate the fraction:
324 = y^2.
Taking the square root of both sides, we find:
y = √324 = 18.
So, the length of the altitude is 18 units.
Now, we can substitute this value of the altitude into the equation x/y = 2/3 to find the length of the base:
x/18 = 2/3.
Cross-multiplying, we get:
3x = 2 * 18.
Simplifying further, we have:
3x = 36.
Dividing both sides by 3, we find:
x = 12.
Therefore, the length of the base is 12 units.