Question

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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

Answer:

Length of first side is :- 18cm ( given )

Length of second side :- Is 5 times greater than first side :- 18 + 5 = 23 cm

Length of third side :- 7 more than first side :- 18 + 7 = 25cm

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$\fbox \red{Now we have }$

First = 18

Second = 23

Third = 25

Semiperemeter = $\dfrac{a + b + c }{2}$

: $\implies$ $\dfrac{18 + 23 + 25 }{2}$

: $\implies$ $\dfrac{66 }{2}$

: $\implies$ $\boxed{\sf{33cm }}$

Therefore, Semiperemeter of given Traingle is 33cm

Answer 2

Given :

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 .

Length of first side is 18 cm .

To Find :

Semi Perimeter of Triangle .

Solution :

\longmapsto\tt{Let\:second\:side\:be=x}⟼Letsecondsidebe=x

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

\longmapsto\tt{First\:side=x-5}⟼Firstside=x−5

Also ,

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

\longmapsto\tt{Length\:of\:third\:side=x-5+7}⟼Lengthofthirdside=x−5+7

Length of first side is 18 cm :

\longmapsto\tt{x-5=18}⟼x−5=18

\longmapsto\tt{x=18+5}⟼x=18+5

\longmapsto\tt\bf{x=23}⟼x=23

Therefore :

\longmapsto\tt{Length\:of\:first\:side=18\:cm}⟼Lengthoffirstside=18cm

\longmapsto\tt{Length\:of\:second\:side=x}⟼Lengthofsecondside=x

\longmapsto\tt\bf{23\:cm}⟼23cm

\longmapsto\tt{Length\:of\:third\:side=23-5+7}⟼Lengthofthirdside=23−5+7

\longmapsto\tt\bf{25\:cm}⟼25cm

For Semi Perimeter :

a = 18 cm

b = 23 cm

c = 25 cm

Using Formula :

\longmapsto\tt\boxed{Semi\:Perimeter=\dfrac{a+b+c}{2}}⟼

SemiPerimeter=

2

a+b+c

Putting Values :

\longmapsto\tt{\dfrac{18+23+25}{2}} ⟼

2

18+23+25

\longmapsto\tt{\cancel\dfrac{66}{2}} ⟼

2

66

\longmapsto\tt\bf{33\:cm}⟼33cm

So , The Semi Perimeter of Triangle is 33 cm .