Question

The perimeter of a triangle is 60cm. If its sides are in the ratio 2:3:5, then its

smallest side is

a) 15 b) 12 c) 30 d)none​

Answer 1

Given thαt,

• The perimeter of α triαngle is 60cm.
• The ratio of sides are 2:3:5.

☯️ We need to find the smαllest side.

__________

To do so,

Let's αssume thαt the sides be 2α, 3α αnd 5α.

According to the question,

:$\implies{\sf{2a+3a+5a=60}}$

:$\implies{\sf{10a=60}}$

:$\implies{\sf{a=\dfrac{60}{10}}}$

:$\large\implies{\boxed{\sf{\orange{6}}}}$

Hence, the sides will be —

• 2(6) = $\large{\overbrace{\sf{\red{12}}}}$
• 3(6) = $\large{\sf{\red{18}}}$
• 5(6) = $\large{\underbrace{\sf{\red{30}}}}$

Hence, the smαllest side will be (b) 12.

And we αre done!

________________________

Answer 2

GiveN:

• perimeter = 60cm

• it's sides ratio = 2:3:5

To FinD:

• smallest side of the triangle?

SolutioN:

$\: \: \: \: \: \: \: \: \: \: \: : \implies \bf 2a + 3a + 5a = 60$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \bf 10a = 60$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \bf a = \cancel{ \frac{60}{10} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies {\boxed{\underline {\green{ \bf a = 6}}}}$

The three sides are:

${ \boxed {\blue{ \bf \: 2 \times 6 = 12cm}}}$

${ \boxed {\pink{ \bf \: 3 \times 6 = 18cm}}}$

${ \boxed {\purple{ \bf \: 5 \times 6 = 30cm}}}$

Thus , the smallest side is 12cm

$\therefore {\red{ \bf The \: smallest \: side \: is \: 12cm \: (b) }}$