Question

the slides of a triangle are x, (x+1) and 13 cm. if its perimeter is 56cm.then find the value of x​

Answer 1

Correct Question-:

• The sides of a triangle are x , (x+1) and 13 cm. If its perimeter is 56cm , Then Find the value of x .

AnswEr-:

• $\boxed{\sf { The\:value \:of\:x = 21\:}}$
• $\boxed{\sf { \:The\:three\:sides\:of\:Triangle \:are\:21cm\:,22cm\;and\:13cm\:}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:First\:side\:of\:triangle\:is\:= \frak{x \: cm}} & \\\\ \sf{The\:Second \:side\:of\:triangle\:is\:= \frak{x +1\: cm}}& \\\\ \sf{The\:Third \:side\:of\:triangle\:is\:= \frak{13\: cm}}& \\\\ \sf{The\:Perimeter \:of\:triangle\:is\:= \frak{56\: cm}}\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:value\:of\:x \:.}\end{cases}$

$\sf{\dag{\underline {Solution\:of\:Question\: -:}}}$

• $\underline{\boxed{\star{\sf{\red{ Perimeter_{(Triangle)}  \: = \: Side _{1}+ Side _{2} + Side_{3}}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{Side_{1}\:or\:First\:Side\:= \frak{x \: cm}} & \\\\ \sf{Side_{2}\:or\:Second\:Side\:= \frak{x +1\: cm}}& \\\\ \sf{Side_{3}\:Third \:side\:= \frak{13\: cm}}& \\\\ \sf{The\:Perimeter \:of\:triangle\:is\:= \frak{56\: cm}}\end{cases}$

• $\sf{\underline {Now,}}$

• $\longrightarrow{\sf { \:x + ( x + 1) + 13 = 56 \:}}$

• $\longrightarrow{\sf { \:x + x + 1 + 13 = 56 \:}}$

• $\longrightarrow{\sf { \:2x+1 + 13 = 56 \:}}$

• $\longrightarrow{\sf { \:2x + 14 = 56 \:}}$

• $\longrightarrow{\sf { \:2x = 56-14 \:}}$

• $\longrightarrow{\sf { \:2x = 42 \:}}$

• $\longrightarrow{\sf { \:x = \dfrac{\cancel {42}}{\cancel {2}}\:}}$

• $\longrightarrow{\sf { \:x = 21\:}}$

Therefore,

• $\boxed{\sf { \:x = 21\:}}$

Now ,

• $\frak{Putting \:x =21\: -:} \begin{cases} \sf{Side_{1}\:or\:First\:Side\:= \frak{x \:=\:21 cm}} & \\\\ \sf{Side_{2}\:or\:Second\:Side\:= \frak{x +1\:=21\:+1=22 cm}}& \\\\ \sf{Dide_{3}\:Third \:side\:= \frak{13\: cm}}\end{cases}$

Hence ,

• $\boxed{\sf { The\:value \:of\:x = 21\:}}$

• $\boxed{\sf { \:The\:three\:sides\:of\:Triangle \:are\:21cm\:,22cm\;and\:13cm\:}}$

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Verification ♡ -:

• $\underline{\boxed{\star{\sf{\red{ Perimeter_{(Triangle)}  \: = \: Side _{1}+ Side _{2} + Side_{3}}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{Side_{1}\:or\:First\:Side\:= \frak{21\: cm}} & \\\\ \sf{Side_{2}\:or\:Second\:Side\:= \frak{22\: cm}}& \\\\ \sf{Side_{3}\:Third \:side\:= \frak{13\: cm}}& \\\\ \sf{The\:Perimeter \:of\:triangle\:is\:= \frak{56\: cm}}\end{cases}$

• $\sf{\underline {Now,}}$

• $\longrightarrow{\sf { \:21 + 22 + 13 = 56 \:}}$

• $\longrightarrow{\sf { \:23 + 13 = 56 \:}}$

• $\longrightarrow{\sf { \:56 = 56 \:}}$

Therefore,

• $\longrightarrow{\sf { \:LHS = RHS \:}}$

• $\longrightarrow{\sf { \:Hence\:Verified \:}}$

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