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

Answer 1

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.