Question

The perimeter of a triangle is 30 cm. Its sides are in the ratio 1 : 3 : 2, then its

smallest side is.

(a) 15 cm

(b) 5cm

(c)1 cm

(4) 10 cm.​

Answer 1

Given that,

• The sides of triangle are in the ratio of 1:3:2.

☯ Let the sides be x, 2x and 3x.

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$

• Perimeter of the triangle is 30 cm.

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Therefore,

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$:\implies\sf x + 2x + 3x = 30 \\\\\\:\implies\sf 6x = 30 \\\\\\:\implies\sf x = \cancel\dfrac{30}{6} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}\:\bigstar$

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$\underline{\bigstar{\textsf{ \: Sides of \: triangle \: are :}}}$

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• First side, x = 5 cm.
• Second side, 2x = 2(5) = 10 cm.
• Third side, 3x = 3(5) = 15 cm

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$\therefore\:{\underline{\sf{Hence,\: smallest \ side \ of \ the \ \triangle \ is \ {\textsf{\textbf{Option b) 5 cm}}}.}}}$

Answer 2

Answer:

Given :-

• Perimeter = 30 cm
• Ratio of sides = 1:3:2

To Find :-

Smallest side

SoluTion :-

As we know that

$\star \frak \red{Perimeter \: = a + b + c }$

Let the ratio be 1x,3x and 2x

$\sf \: 30 = 1 x + 3x + 2x$

$\sf \: 30 = 6x$

$\sf \: x \: = \cancel\dfrac{30}{6}$

$\frak \red{x \: = 5}$

Smallest side will be

$\sf \implies \: 5 \: cm \: (option \: b)$