The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If its perimeter is 52 cm, the length of the smallest side is :

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RRB ASSISTANT LOCO PILOT (Patna) 2013 click here to view all questions

The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If its perimeter is 52 cm, the length of the smallest side is :

A9 cm

B10 cm

C11 cm

D12 cm

rihad ? Jan 8 '2020 at 10:44

Correct answer is: 12 cm

Explanation:

\(\text{Let the sides be } \frac{1}{2}x, \frac{1}{3}x,\frac{1}{4}x\)

\(\text{Perimeter }= a+b+c\)

\(52cm = \frac{1}{2}x+\frac{1}{3}x+\frac{1}{4}x\)
 
\(52cm= \frac{(6x+4x+3x)}{12}\)

\(52= \frac{13}{12}x\)

\(\frac{52\times12}{13}=x\)

\(4\times12=x=48\)

\(\text{Sides are }\frac{1}{2}\times48=24cm;\)
\(\frac{1}{3}\times48=18cm;\)
\(\frac{1}{4}\times48=12cm\)

\(\therefore \text{12 cm is the smallest side}\)

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Correct answer is: 12 cm Explanation: \(\text{Let the sides be } \frac{1}{2}x, \frac{1}{3}x,\frac{1}{4}x\) \(\text{Perimeter }= a+b+c\) \(52cm = \frac{1}{2}x+\frac{1}{3}x+\frac{1}{4}x\)   \(52cm= \frac{(6x+4x+3x)}{12}\) \(52= \frac{13}{12}x\) \(\frac{52\times12}{13}=x\) \(4\times12=x=48\) \(\text{Sides are }\frac{1}{2}\times48=24cm;\) \(\frac{1}{3}\times48=18cm;\) \(\frac{1}{4}\times48=12cm\) \(\therefore \text{12 cm is the smallest side}\) rihad ? answered Jan 8 '2020 at 10:44 All Comments

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