question_answer

Hypotenuse of a right triangle is \[\text{25 cm}\] and out of the remaining two sides, one is longer than the other by \[\text{5 cm}\]. Then the length of the longer side is:

A) \[20\,cm\]

B) \[15\,cm\]

C) \[12.5\,cm\]

D) \[10\,cm\]

Correct Answer: A

Solution :

Consider the right triangle ABC as shown    below.

Let \[BC=x\,cm,\] then \[AB=(x+5)\,cm.\]

As ABC is a right triangle, applying

Pythagoras theorem, we get.

\[{{25}^{2}}={{x}^{2}}+{{(x+5)}^{2}}\]

Therefore,    \[625={{x}^{2}}+{{x}^{2}}+10x+25\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,2{{x}^{2}}+10x-600=0\,\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,{{x}^{2}}+5x-300=0\,\]

Factorizing by splitting the middle term.

\[{{x}^{2}}+20x-15x-300=0\]

\[\Rightarrow \,\,\,\,\,x(x-20)-15(x+20)=0\Rightarrow x=15,\,x=-20\] As length cannot be negative,

Therefore,  and .

Length of the longer side

So, option [a] is correct.