Question

The semiperimeter of a triangle is 20 cm and the length of its two sides is 12 cm each . What is the length of its remaining side?

Answer 1

S = 20
Sum of two sides = 24
Other side = x
(12+12+x)/2 = 20
24+x = 40
x = 16

Answer 2

Correct Question-:

The semiperimeter of a triangle is 20 cm and the length of its two sides is 12 cm each . What is the length of its remaining side ?

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ Side _{3}\:or\:Remaining \:Side\:of\:Triangle \:is\:of\:16cm\:.}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\: Semi Perimeter \:of\:a\:triangle \:is\:= \frak{20cm}} & \\\\ \sf{ \:\:The \:length\: of \:its\: two \:sides \:is \frak{12cm}}\end{cases}$

• $\frak{Given \:\: -:} \begin{cases} \sf{The \:length\: of \:its\: Remaining \:sides \:.}\end{cases}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{ Semi\:Perimeter \:_{(Triangle)}\: \frac{Side_{1}+ Side_{2}+Side _{3}}{2}\:.}}}}}$

• $\frak{Given \:\: -:} \begin{cases} \sf{The\: Semi Perimeter \:of\:a\:triangle \:is\:= \frak{20cm}} & \\\\ \sf{ \:\:Side_{(1)}=\frak{12cm}}& \\\\ \sf{ \:\:Side_{(1)}=\frak{12cm}}& \\\\ \sf{ \:\:Side_{(3)}=\frak{??}}\end{cases}$

Now,

• $\implies{\sf{\large { Semi \:Perimeter\:= \frac{12+12+Side_{3}}{2}= 20 cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= \frac{24+Side_{3}}{2}= 20 cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= 24+Side_{3}= 20 × 2}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= 24+Side_{3}= 40cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= Side_{3}= 40-24}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= Side_{3}= 16cm}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ Side _{3}\:=\:16cm\:.}}}}}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ Side _{3}\:or\:Remaining \:Side\:of\:Triangle \:is\:of\:16cm\:.}}}}}$

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♤Verification ♤

• $\underline{\boxed{\star{\sf{\blue{ Semi\:Perimeter \:_{(Triangle)}\: \frac{Side_{1}+ Side_{2}+Side _{3}}{2}\:.}}}}}$

• $\frak{Given \:\: -:} \begin{cases} \sf{The\: Semi Perimeter \:of\:a\:triangle \:is\:= \frak{20cm}} & \\\\ \sf{ \:\:Side_{(1)}=\frak{12cm}}& \\\\ \sf{ \:\:Side_{(1)}=\frak{12cm}}& \\\\ \sf{ \:\:Side_{(3)}=\frak{16cm}}\end{cases}$

Now,

• $\implies{\sf{\large { Semi \:Perimeter\:= \frac{12+12+16}{2}= 20 cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= \frac{24+16}{2}= 20 cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= \frac{40}{2}= 20 cm}}}$
• $\implies{\sf{\large { Semi \:Perimeter\:= 20cm= 20 cm}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ LHS \: = \: RHS\:.}}}}}$
• $\underline{\boxed{\star{\sf{\blue{ Hence \: ,\: Verified \:.}}}}}$

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