Question

A right triangle has hypotenuse of length p cm and one side of length q cm. If p-q = 1, express length of the third side of the right triangle in term of p is

• A. $\sqrt{2p-1}cm$
• B. $\sqrt{2p}$
• C. $\sqrt{p-1}$
• D. none of these

Answer 1

The correct option is A $\sqrt{2p-1}cm$

Solution :- given

$\Rightarrow$ for right angle triangle

hypotenuse $=pcm$

one side $=qcm$

and, $p-q=1$

$-q=1-p$

$\Rightarrow q=p-1$

By pythagoros Theorem

$\Rightarrow p^2=q^2+x^2$ (x is the remaining side)

$\Rightarrow x=\sqrt{p^2-q^2}$

$=\sqrt{p^2-(p-1{)}^2}=\sqrt{p^2-p^2-1+2p}$

$=\sqrt{2p-1}cm$ (Ans)