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

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 :

⟼Letsecondsidebe=x

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

⟼Firstside=x−5

Also ,

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

⟼Length of third side=x−5+7

Length of first side is 18 cm :

$\longmapsto\tt{x-5=18}$

$\longmapsto\tt{x=18+5}$

$\longmapsto\tt\bf{x=23}$

Therefore :

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

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

$\longmapsto\tt\bf{23\:cm}$

$</p><p>\longmapsto\tt{Length\:of\:third\:side=23-5+7}$

⟼Length of third side=23−5+7

$\longmapsto\tt\bf{25\:cm}$

For Semi Perimeter :

a = 18 cm

b = 23 cm

c = 25 cm

Using Formula :

$</p><p>\longmapsto\tt\boxed{Semi\:Perimeter=\dfrac{a+b+c}{2}}$

Putting Values :

$\longmapsto\tt{\dfrac{18+23+25}{2}}$

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

$\longmapsto\tt\bf{33\:cm}$

So , The Semi Perimeter of Triangle is 33 cm .

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 :

⟼Letsecondsidebe=x

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

⟼Firstside=x−5

Also ,

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

⟼Length of third side=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

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

⟼Length of third side=23−5+7

\longmapsto\tt\bf{25\:cm}⟼25cm

For Semi Perimeter :

a = 18 cm

b = 23 cm

c = 25 cm

Using Formula :

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

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 .