Question

The hypotenuse of a right angled triangle is$25cm$. The other two sides are such that one is $5cm$ longer than the other. Their lengths (in cm) are:

• A. $10,15$
• B. $20,25$
• C. $15,20$
• D. $25,30$

Answer 1

The correct option is C

$15,20$

Step 1

Hypotenuse of right triangle$=25cm$

Let us assume the other sides be$x$and $x+5$

Step 2

By Pythagoras Theorem:

$$\begin{gathered} {25}^2=x^2+{(x+5)}^2 \\ 625=x^2+x^2+25+10x \\ 2x^2+10x–600=0 \end{gathered}$$

Taking$2$ as common, we get,

$$\begin{gathered} x^2+5x–300=0 \\ {x}^2+20x–15x–300=0 \\ x(x+20)–15(x+20)=0 \\ (x+20)(x–15)=0 \\ x=-20,x=15 \end{gathered}$$

But$x$cannot be negative

Therefore, one side$=x=15cm$

Other side$=x+5=15+5=20cm$

Hence, the other two sides are $15cm,20cm$

So, the correct option is (C)