Question

The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

Answer 1

Let one hypotenuse of the triangle be x cm.
From the given information,
Length of one side = (x – 1) cm
Length of other side = (x – 18) cm
Using Pythagoras theorem,
$x^2=(x–1{)}^2+(x–18{)}^2$
$x^2=x^2+1–2x+x^2+324–36x$
$x^2–38x+325=0$
$x2–13x–25x+325=0$
$x(x–13)–25(x–13)=0$
$(x–13)(x–25)=0$
$x=13,25$
When x = 13, x – 18 = 13 – 18 = -5, which being negative, is not possible.
So, x = 25
Thus, the lengths of the sides of the triangle are x = 25 cm, (x – 1) = 24 cm and (x – 18) = 7 cm.