The area of a right angled triangle is 96cm^2. If the two shorter sides of the triangle differ by 2 what is the length of the shorter side
Let the two shorter sides of the triangle be x and x + 2.
The area of a right angled triangle is given by the formula:
Area = (1/2) * base * height
Since the triangle is right angled, one of the shorter sides is the base and the other shorter side is the height.
So, the equation becomes:
96 = (1/2) * x * (x + 2)
Simplifying the equation:
192 = x * (x + 2)
Expanding and rearranging:
x^2 + 2x - 192 = 0
We can solve this quadratic equation by factoring or using the quadratic formula.
Let's factorize the equation:
(x + 16)(x - 12) = 0
Setting each factor equal to zero:
x + 16 = 0 or x - 12 = 0
So, x = -16 or x = 12
Since the length cannot be negative, we use x = 12.
Therefore, the length of the shorter side is 12 cm.