Math, asked by vinod111154, 4 months ago

the semi- perimeter of a triangle is 10 cm . if one of its side is 5cms and 7 cms respectively then its third side is ​

Answers

Answered by ShírIey
171

Appropriate Question:

  • Two sides of a triangle are 5 cm and 7 cm and its semi-perimeter is 10 cm. Then the third side of the triangle is?

Given:

  • Semi Perimeter of a triangle is 10 cm.
  • Two sides of triangle are 5 cm and 7 cm respectively.

To find:

  • The third side of the triangle.

Solution: Let the third side of the triangle be c cm and other sides be a is 5 cm and b is 7 cm respectively.

As we know that,

Semi perimeter = Sum of all sides (a + b + c)/2

\implies S = 5 + 7 + c/2

\implies 10 = 12 + c/2

\implies c = 20 - 12

\implies c = 8 cm

•°• Hence, the third side of the triangle is 8 cm.

\rule{200}2

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ MORE TO KNOW :

  • A triangle is a shape with the three straight sides.

  • Sum of all angles of the triangle is 180°.

  • Area of right triangle = 1/2 × (Base) × (Height)

  • Perimeter of triangle = (a + b + c). Here, a, b and c are the sides of triangle.
Answered by Anonymous
130

Answer:

Given :-

  • The semi-perimeter of a triangle is 10 cm. One of its side is 5 cm and 7 cm respectively.

To Find :-

  • What is the third side of a triangle.

Formula Used :-

\sf\boxed{\bold{Semi-perimeter\: =\: \dfrac{Sum\: of\: all\: sides\: of\: triangle}{2}}}

Solution :-

Let, the third side of a triangle be c cm.

Given :

  • First side (a) = 5 cm
  • Second side (b) = 7 cm

According to the question by using the formula we get,

\sf 10 =\: \dfrac{5 + 7 + c}{2}

\sf 10 =\: \dfrac{12 + c}{2}

\sf c =\: 2 \times 10 - 12

\sf c =\: 20 - 12

\sf\bold{\pink{c =\: 8\: cm}}

\therefore The third side of a triangle is 8 cm .

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