Question

The hypotenuse of a right triangle is 25 cm. The other two sides are such that one is 5 cm longer. The lengths of these sides are
(a) 10 cm, 15 cm
(b) 15 cm, 20 cm
(c) 12 cm, 17 cm
(d)13 cm, 18 cm

Answer 1

(b) 15 cm, 20 cm

It is given that the length of hypotenuse is 25 cm.
Let the other two sides be x cm and (x$-$5) cm.
Applying Pythagoras theorem, we get:

$$\begin{gathered} {25}^2=x^2+(x-5{)}^2 \\ \Rightarrow 625=x^2+x^2+25-10x \\ \Rightarrow 2x^2-10x-600=0 \\ \Rightarrow x^2-5x-300=0 \\ \Rightarrow x^2-20x+15x-300=0 \\ \Rightarrow x\left(x-20\right)+15\left(x-20\right)=0 \\ \Rightarrow (x-20\left)\right(x+15)=0 \\ \Rightarrow x-20=0orx+15=0 \\ \Rightarrow x=20\mathrm{or}x=-15 \\ \mathrm{Side}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{cannot}\mathrm{be}\mathrm{negative}. \\ \mathrm{Therefore},x=20\mathrm{cm} \end{gathered}$$

Now,
x $-$ 5 = 20 $-$ 5 = 15 cm