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?​

Answer 1

Solution!!

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

Length of the first side = Length of second side - 5 cm

It is given that the length of the first side is 18 cm.

18 cm = Length of second side - 5 cm

Length of second side = 18 cm + 5 cm

Length of the second side = 23 cm

Length of the third side is 7 cm more than length of the first side.

Length of third side = 7 cm + Length of first side

Length of third side = 7 cm + 18 cm

Length of third side = 25 cm

Let the side a = 18 cm

Let the side b = 23 cm

Let the side c = 25 cm

Semi-perimeter (s) = (a + b + c)/2

s = (18 cm + 23 cm + 25 cm)/2

s = (66 cm)/2

s = 33 cm

Semi-perimeter of the triangle = 33 cm

Answer 2

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,

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

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,

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

Thus ,

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

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

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

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

Where,

• A , B & C are three sides of Triangle.

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

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

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

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

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

Therefore,

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

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