The height of the triangle is 4 inches greater than the base the area of the triangle is 96 square inches find the length of the base and the height of the triangle
Let's assume that the base of the triangle is x inches.
Then, the height is (x+4) inches.
The area of a triangle is given by the formula: Area = (1/2) * base * height.
In our case, the area is 96 square inches, so we can write the equation:
96 = (1/2) * x * (x+4)
Simplifying this equation, we get:
192 = x * (x+4)
Expanding the equation, we get:
192 = x^2 + 4x
Rearranging the equation, we get:
x^2 + 4x - 192 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula. Factoring gives us:
(x-12)(x+16) = 0
So, we have two possible solutions:
x-12 = 0 or x+16 = 0
If x-12 = 0, then x = 12.
If x+16 = 0, then x = -16.
Since the base of the triangle cannot be negative, we can ignore the second solution.
Therefore, the length of the base of the triangle is 12 inches.
The height of the triangle is (12+4) = 16 inches.