Question

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.

Answer 1

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 .