Subject: General Aptitude · Chapter: Area · Exam: 2005 · Marks: · Difficulty:
The sides of a triangle are in the ratio of $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$. If the perimeter is 52 cm, then the length of the smallest side is
(a)9 cm
(b)10 cm
(c)11 cm
(d)12 cm
Answer
Answer (as printed): D
Explanation
Ratio of sides $=\frac{1}{2}: \frac{1}{3}: \frac{1}{4}=6: 4: 3$. Perimeter = 52 cm. So, sides are $$\left(52 \times \frac{6}{13}\right) \mathrm{cm},\left(52 \times \frac{4}{13}\right) \mathrm{cm} \text { and }\left(52 \times \frac{3}{13}\right) \mathrm{cm} .$$ So, $a=24 \mathrm{cm}, b=16 \mathrm{cm}, c=12 \mathrm{cm}$. $$\text { ∴ Length of smallest side }=12 \mathrm{cm} \text {. }$$