The hypotenuse (in cm) of a right angled triangle is . . .

Question  : The hypotenuse (in cm) of a right angled triangle is 6cm more than twice the length of  the shortest side. If the length of third side is 6 cm less than thrice the length of the shortest side, then find the dimensions of the triangle.

Dobut by CBSE 

Solution : 

Let the shortest of the right angled triangle = x cm

Hypotenuse = (6+2x) cm 

Third side = (3x-6) cm 

Using Pythagoras Theorem 

H²=P²+B²

(6+2x)²=(x)²+(3x-6)²
36+4x²+24x=x²+9x²+36-36x

4x²+24x=10x²-36x

0=10x²-36x-4x²-24x
0=6x²-60x
0=6(x²-10x)
0/6=(x²-10x)
0=x(x-10)
x=0 OR x-10=0
x=0 OR x=10

But x≠0
∴ x=10 cm

Now, 
Shortest side = x = 10 cm

Hypotenuse = (6+2x) cm
= [6+2(10)]

= [6+20]
= 26 cm

Third Side = [3x-6] cm
= [3(10)-6] cm

= [30-6] cm

= 24 cm

Hence, the required dimensions of right angled triangle are 10 cm, 24 cm and 26 cm.