Question

${\tt{\red{\underline{\underline{\huge{QuesTion}}}}}}$
In a triangle , the length of the first side is 5 cm less than the length of the second side . The length of the third side is 7 cm more than the length of the first side if the first side is of length is 18 cm , then what is the semiperimeter of the triangle?
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Answer 1

$\huge\bold{Given}$

In a triangle , the length of the first side is 5 cm less than the length of the second side . The length of the third side is 7 cm more than the length of the first side if the first side is of length is 18 cm .

Need To Find : Semi-Perimeter of Triangle .

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❒ Let's consider A , B & C be the three sides of Triangle.

⠀⠀⠀⠀⠀Finding Sides of Triangle :

First Side or A of Triangle :

First Side or A of Triangle is 18 cm . [ Given That ]

Second Side or B of Triangle :

Given that ,

The length of the first side is 5 cm less than the length of the second side .

Then ,

Second Side = First Side + 5

Or ,

Second Side = 18 + 5

Second Side = 23 cm

Therefore,

⠀⠀⠀⠀$⠀\begin{gathered}\therefore {\underline{ \mathrm { Second \:Side\:or\:B\:of\:Triangle \:is\:\bf{23\: cm}}}}\\\end{gathered}$

Third Side or C of the Triangle :

Given that,

The length of the third side is 7 cm more than the length of the first side

Then ,

Third Side = First Side + 7

Or ,

Third Side = 18 + 7

Third Side = 25 cm .

Therefore,

⠀⠀⠀⠀$⠀\begin{gathered}\therefore {\underline{ \mathrm { Third \:Side\:or\:C\:of\:Triangle \:is\:\bf{25\: cm}}}}\\\end{gathered}$

Thus ,

⠀⠀⠀$⠀⠀\begin{gathered}\therefore {\underline{ \mathrm { The\:Length \:of\:all\:three \:of\:Triangle \:are\:\bf{18\:cm,\:23cm\:\& 25cm}}}}\\\end{gathered}$

⠀⠀⠀⠀⠀ Finding Semi-Perimeter of Triangle :

$\begin{gathered}\frak {\underline {\dag As \:We\:know\:that\::}}\\\end{gathered}$

$\begin{gathered}\star\boxed {\sf{\pink { Semi-Perimeter \:= \dfrac{A + B + C}{2}}}}\\\end{gathered}$

Where,

A , B & C are three sides of Triangle.

⠀⠀⠀⠀⠀$⠀\begin{gathered}\underline {\bf{\star\:Now \: By \: Substituting \: the \: Found \: Values \::}}\\\end{gathered}$

$\begin{gathered}\qquad \qquad :\implies \sf{ Semi-Perimeter \:= \dfrac{18 + 23 + 25 }{2} }\\\end{gathered}$

$\begin{gathered}\qquad \qquad :\implies \sf{ Semi-Perimeter \:= \dfrac{18 + 48 }{2} }\\\end{gathered}$

$\begin{gathered}\qquad \qquad :\implies \sf{ Semi-Perimeter \:= \cancel{\dfrac{66 }{2}} }\\\end{gathered}$

⠀⠀⠀⠀$⠀\begin{gathered}\underline {\boxed{\pink{ \mathrm { Semi-Perimeter = 33\: cm}}}}\:\bf{\bigstar}\\\end{gathered}$

Therefore,

⠀⠀⠀⠀$⠀\begin{gathered}\therefore {\underline{ \mathrm { Semi-Perimeter \:of\:Triangle \:is\:\bf{33\: cm}}}}\\\end{gathered}/$

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