Question

The perimeter of triangle is 30 cm. it's side are in the ratio 1:3:2 find its smallest side​

Answer 1

Given:-

• The perimeter of a triangle is 30 cm.
• It's side are in the ratio 1:3:2.

To find:-

• Its smallest side.

Solution:-

Let,

• the sides of a triangle be 1x, 3x, and 2x.

According to the question,

→ 1x + 3x + 2x = 30

→ 4x + 2x = 30

→ 6x = 30

→ x = 30/6

→ x = 5 cm

Hence,

• the smallest side of a triangle is 5 cm.

Answer 2

Given : The perimeter of triangle is 30 cm and it's side are in the ratio 1:3:2 .

Need to Find : The smallest side of triangle.

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$\sf{\bf{Solution \:of\:Question \::}}$ Let's Assume the three sides of Triangle be 1x , 3x and 2x respectively .

$\qquad \quad \qquad \qquad \implies {\mathrm {Perimeter_{(Triangle)} = Side A + Side\:B+ Side\:C }}$

⠀⠀⠀⠀⠀ As We have Assumed the measure of all three side of Triangle [ Side A = 1 x , Side B = 3x and Side C =2x] and Given Perimeter of Triangle is 30 cm By Substituting the Assumed value and Given value in the Formula we can find the measure of all three sides of Triangle and when we find measures of all three sides then from there we can find the smallest sside of Triangle.

⠀⠀⠀⠀⠀$\underline {\star{\mathrm {\bf { Now \:By\:Substituting \:the \:Values\:,}}}}$

⠀⠀⠀⠀⠀$\implies {\mathrm { 1x + 3x + 2x = 30 }}$

⠀⠀⠀⠀⠀$\implies {\mathrm { 1x + 5x = 30 }}$

⠀⠀⠀⠀⠀$\implies {\mathrm { 6x = 30 }}$

⠀⠀⠀⠀⠀$\implies {\mathrm { x =\dfrac {\cancel {30}}{\cancel {6}} }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{\mathrm { x = 5\:cm }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀$\underline {\star{\mathrm {\bf { Now \:By\:Substituting \:the \:Value\:of\:x\:in\:Assumed\:sides,}}}}$

⠀⠀⠀⠀⠀Side A or First Side of Triangle = 1x = 1 × 5 = 5 cm

⠀⠀⠀⠀⠀Side B or Second Side of Triangle = 3x = 3 × 5 = 15 cm

⠀⠀⠀⠀⠀Side C or Third Side of Triangle = 2x = 2 × 5 = 10 cm

$\underline {\sf{\pink{Hence,\:The\:smallest \:side\:of\:triangle \:is\:of\:5\:cm\:}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large{\bf{\mathrm { Verification \::}}}$

As , We know that ,

⠀⠀⠀⠀⠀ $\implies {\mathrm { L.H.S \: = 30\:cm }}$

⠀⠀⠀⠀⠀$\underline {\star{\mathrm {\bf { Now \:By\:Finding \:R.H.S\:,}}}}$

⠀⠀⠀⠀⠀$\implies {\mathrm { R.H.S \:= 5 + 15 + 10 }}$

⠀⠀⠀⠀⠀$\implies {\mathrm { R.H.S \:= 30\:cm }}$

Therefore,

⠀⠀⠀⠀⠀$\mathrm {\bf{ L.H.S = R.H.S }}$

⠀⠀⠀⠀⠀$\dag{\quad \mathrm {\bf{ Hence ,\: Verified \:}}}$

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