Question

two sides of a triangle are 13 cm and 14 cm and its semi perimeter is 18 cm then what will be the third side of the triangle

Answer 1

since ,

Semi-perimeter of a triangle = $\bf{\frac{Sum\: of\: all\: sides}{2}}$

then,

let ,

$\bf{a = side 1 = 13 cm}$

$\bf{b = side 2 = 14 cm}$

And, $\bf{c = side 3 = ?}$

Also ,

semi-perimeter = $\bf{\frac{a + b + c}{2}}$

=> $\bf{18cm}$ = $\bf{\frac{13 + 14 + c}{2}}$

=> $\bf{18}$ = $\bf{\frac{27 + c}{2}}$

Now, take 2 to other side as it is dividing, so taking other side it will multiply!

=> $\bf{18 \times 2}$ = $\bf{27 + c}$

=> $\bf{36}$ = $\bf{27 + c}$

take 27 to other side as it is positive, so taking other side it will become negative!

=> $\bf{36 - 27}$ = $\bf{c}$

=> $\bf{9 cm}$ = $\bf{c}$

$\therefore$Third side =$\boxed{\huge{ c \:= \:9\: cm}}$

★ $\texttt{\huge{\underline{Be\: brainly!}}}$ ★

Answer 2

${\boxed {\boxed { \sf {Here's \: the \: answer}}}}$

Given =>

Two sides of triangle = 13 cm and 14 cm respectively

Semi perimeter = 18

To find =>
Third side of the triangle = ?

Solution =>

Let the first side of the triangle be 'a' ,
second side be 'b' ,
third side be 'c' .

We know that,

Semi perimeter of triangle $\sf { = \frac{ a \: + \: b \: + \: c}{2}}$

$\sf{ 18= \frac{13 \: + \: 14 \: + \: c}{2}}$

$\sf{18 = \frac{27 \: + \: c}{2}}$

Now,

Taking the denominator 2 to the L.H.S

$\sf{18 \times 2 = 27 + c}$

$\sf{36 = 27 + c}$

Now, Taking the term 27 to the L.H.S

$\sf{36 - 27 = c}$

$\sf{9 = c}$

Thus,

The third side of the triangle is 9 cm

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Thanks!