If the hypotenuse of a right-angled triangle is 41 cm and the area of the triangle is 180 sq. cm, then the… · ABC26GN4473
Subject: General Aptitude · Chapter: Area
If the hypotenuse of a right-angled triangle is 41 cm and the area of the triangle is 180 sq. cm, then the difference between the lengths of the legs of the triangle must be
(a)22 cm
(b)25 cm
(c)27 cm
(d)31 cm
Answer
Answer (as printed): D
Explanation
Let the base be $b$ cm and height be $h$ cm. Then, $\frac{1}{2} b h=180 \Rightarrow b h=360$. And, $b^{2}+h^{2}=(41)^{2} \Rightarrow b^{2}+h^{2}=1681$. $$\begin{aligned} & \therefore \quad(b-h)^{2}=b^{2}+h^{2}-2 b h=1681-720=961 \\ & \Rightarrow(b-h)=\sqrt{961}=31 \mathrm{cm} . \end{aligned}$$