The lengths of the two legs of a right triangle are x m and (x+9) m, while its hypotenuse is 45 m. What is the length of the shorter leg?

Correct answer: 27 मीटर

By the Pythagorean theorem, \(x^2+(x+9)^2=45^2\). Simplifying gives \(x^2+9x-972=0\), which factors as \((x-27)(x+36)=0\). Thus, \(x=27\) or \(x=-36\). Since a length cannot be negative, the shorter leg is 27 m. Exam tip: Reject any negative root when the variable represents a length.