Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
If the perimeter of a right-angled isosceles triangle is $(4 \sqrt{2}+4) \mathrm{cm}$, the length of the hypotenuse is
(a)4 cm
(b)6 cm
(c)8 cm
(d)10 cm
Answer
Answer (as printed): A
Explanation
Let the length of each of the sides containing the right angle be $x$ cm. Then, hypotenuse $=\sqrt{x^{2}+x^{2}} \mathrm{cm}=\sqrt{2 x^{2}} \mathrm{cm}=\sqrt{2} x \mathrm{cm}$. Perimeter of the triangle $=(x+x+\sqrt{2} x) \mathrm{cm}=(2 x+\sqrt{2} x) \mathrm{cm}$ $$=\sqrt{2} x(\sqrt{2}+1) \mathrm{cm} .$$ $\therefore \sqrt{2} x(\sqrt{2}+1)=(4 \sqrt{2}+4)=4(\sqrt{2}+1) \Rightarrow \sqrt{2} x=4 \Rightarrow x=2 \sqrt{2}$. Hence, hypotenuse $=(\sqrt{2} \times 2 \sqrt{2}) \mathrm{cm}=4 \mathrm{cm}$.