Question

In a right angle triangle ,the hypotenuse is 10 cm more than the shortest side. If third side is 6 CM less than the hypotenuse, find the sides of the right angle triangle​

Answer 1

I also believe that this question contains incorrect values.

According to this question, the final equation you will get is

x² - 12x - 84 = 0 (I took the shortest side as x cm)

The values of x you will get are irrational and those will be (by quadratic formula),

x = (12 +/- √480)/2 cm

Answer 2

Sides of the right angle triangle​:

Shorter side = 16.955 cm

Hypotenuse = x + 10 = 16.955 + 10 = 26.955 cm

Third side = x + 4 = 16.955 + 4 = 20.955 cm

Step-by-step explanation:

From question, the shape is a right angled triangle.

On applying Pythagoras theorem, we get,

(Hypotenuse)² = (Base)² + (Height)² → (Equation 1)

From question, let the unknown side be 'x'.

Shorter Side = x cm

Hypotenuse = x + 10 cm

Third Side = hypotenuse - 6 cm =  x + 10 - 6 = x + 4 cm

On substituting the values in equation (1), we get,

(x + 10)² = x² + (x + 4)²

x² + 100 + 20x = x² + x² + 16 + 8x

x² + 100 + 20x = 2x² + 16 + 8x

(2 - 1)x² + (8 - 20)x + (16 - 100) = 0

x² - 12x - 84 = 0

The value of x is given as:

x = (b ± √(b² - 4ac))/2a

x = (12 ± √(144 + 336))/2

x = (12 ± 21.91)/2

x = 16.955 and -4.955

Since, x cannot be negative then the value of x is 16.955 cm.