The base of a triangle is 3m longer than the height. Find the base if the area of this triangle is 77m^2.
Find the area of triangle if the base is 6m and the height is 3m.
To find the base of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) * base * height
We are given that the area of the triangle is 77m^2. Let's substitute this value into the formula:
77m^2 = (1/2) * base * height
Now, let's work with the other information provided. We are told that the base of the triangle is 3m longer than the height. We can represent this relationship as:
base = height + 3m
Now, let's substitute this expression for the base in the equation:
77m^2 = (1/2) * (height + 3m) * height
Simplifying further:
154m^2 = (height + 3m) * height
To solve for height, we can rearrange the equation into a quadratic form:
0 = height^2 + 3height - 154
Now we have a quadratic equation that we can solve using factoring, completing the square, or the quadratic formula. In this case, let's use factoring.
0 = (height - 7)(height + 22)
Setting each factor equal to zero gives:
height - 7 = 0 or height + 22 = 0
height = 7 or height = -22 (extraneous solution)
Since height cannot be negative, we discard the extraneous solution.
We found that the height of the triangle is 7m. Now we can substitute this value back into the expression for the base:
base = height + 3m
base = 7m + 3m
base = 10m
Therefore, the base of the triangle is 10m.
Area = 1/2 base * Height
Base = height - 3
77 = 1/2 (height - 3)(height)
Solve for height and put that value into the second equation. Check by putting both values into the second equation.