# The hypotenuse of a right–angled triangle is 6 cm more than twice the shortest side. If the third side is 2 cm less than the hypotenuse, find the sides of the triangle.

Let the shortest side(AC) be ‘(X)’cms, so the hypotenuse (BC) will be ‘(2X+6)’ cms, as demonstrated in the figure drawn below: AB = 2X + 4 cms

(BC)2 = (AC)2 + (AB)2

(2X + 6)2 = X2 +(2X + 4)2

On simplifying further,

4X2 + 24X + 36 = X2 + 4X2 + 16X + 16

Using the identity of a2 + b2 + 2ab = (a + b)2

X2 – 8X – 20 = 0 –––––– (i)

On applying Sreedhracharya formula     X = –2 or 10.

the shortest side (AC) is X = 10 cms (Only positive values), hypotenuse (2X+6) i.e., (BC) is 26 cms and the other side (AB) is (2X+4) i.e., 24 cms .

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