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

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 :

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

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

$\longmapsto\tt{First\:side=x-5}$

Also ,

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

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

Length of first side is 18 cm :

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

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

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

Therefore :

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

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

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

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

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

For Semi Perimeter :

• a = 18 cm
• b = 23 cm
• c = 25 cm

Using Formula :

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

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

Answer:

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 first side.
• First side is of length is 18 cm.

To Find :-

• What is the semi-perimeter of the triangle.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Semi-perimeter (S) =\: \dfrac{a + b + c}{2}}}}$

where,

• a = First side
• b = Second side
• c = Third side

Solution :-

So, first we have to find the side of the triangle,

Let, according to the question,

$\mapsto$ Second side = x cm

$\mapsto$ First side = x - 5 cm

And,

$\mapsto$ Third side = x - 5 + 7 cm

According to the question,

⇒ $\sf x - 5 =\: 18$

⇒ $\sf x =\: 18 + 5$

➠ $\sf\bold{\green{x =\: 23\: cm}}$

Hence, the sides of a triangle are :

➲ First side of a triangle :

↦ $\sf x - 5 \: cm$

↦ $\sf 23 - 5\: cm$

➦ $\sf\bold{\purple{18\: cm}}$

➲ Second side of a triangle :

↦ $\sf x\: cm$

➦ $\sf\bold{\purple{23\: cm}}$

And,

➲ Third side of a triangle :

↦ $\sf x - 5 + 7\: cm$

↦ $\sf 23 - 5 + 7\: cm$

↦ $\sf 18 + 7\: cm$

➦ $\sf\bold{\purple{25\: cm}}$

Now, we have to find the semi-perimeter of a triangle,

Given :

• First side (a) = 18 cm
• Second side (b) = 23 cm
• Third side (c) = 25 cm

According to the question by using the formula we get,

$\implies \sf Semi-perimeter\: (S) =\: \dfrac{18 + 23 + 25}{2}$

$\implies \sf Semi-perimeter\: (S) =\: \dfrac{41 + 25}{2}$

$\implies \sf Semi-perimeter\: (S) =\: \dfrac{\cancel{66}}{\cancel{2}}$

$\implies \sf\bold{\red{Semi-perimeter\: (S) =\: 33\: cm}}$

$\therefore$ The semi-perimeter of a triangle is 33 cm.