Math, asked by Anonymous, 7 months ago

The perimeter and area of a triangle whose sides are of length 3cm , 4cm , and 5cm respectively are - A) 12 cm , 6 cm square B) 12 cm , 12 cm square C) 6 cm , 6 cm square D) 6 cm , 12 cm square

Answers

Answered by Anonymous
60

Answer :

The perimeter of the triangle is 12 cm and the area of the triangle is 6 cm.

Given :

  • 3 sides of the triangle is 3 cm , 4 cm and 5 cm respectively.

To find :

  • Perimeter and area of the triangle.

Solution :

Consider,

  • 3 sides of the triangle is a cm, b cm and c cm respectively.

Formula used :-

{\boxed{\sf{Perimeter\:of\: triangle=a+b+c}}}

Then,

Perimeter of the triangle,

= (3+4+5) cm

= 12 cm

Therefore, perimeter of the triangle is 12 cm.

Formula Used :-

{\boxed{\sf{Area\:of\: triangle=\sqrt{s(s-a)(s-b)(s-c)}}}}

Where,

  • a = 3 cm
  • b = 4 cm
  • c = 5 cm
  • s = 12/2 = 6 cm

Area of the triangle ,

= \sf{\sqrt{s(s-a)(s-b)(s-c)}}

= \sf{\sqrt{6(6-3)(6-4)(6-5)}} cm²

= \sf{\sqrt{6\times\:3\times\:2\times\:1}} cm²

= \sf{\sqrt{36}} cm²

= 6 cm²

Therefore , the area of the triangle is 6 cm².

{\boxed{\sf{Option (A)\:is\:correct.}}}

Answered by MaIeficent
92

Step-by-step explanation:

\bf{\underline{\underline\red{Given:-}}}

  • The sides of the triangle are

  • 3cm , 4cm and 5cm.

\bf{\underline{\underline\blue{To\:Find:-}}}

  • The perimeter of the triangle.

  • The area of the triangle.

\bf{\underline{\underline\green{Solution:-}}}

As we know that:-

The perimeter of the triangle is given by the formula:-

\boxed{ \rm Perimeter \: of \:  the \: triangle = a + b + c}

Here:-

• a , b and c are the sides of the triangle.

Now

Perimeter of the triangle

= 3 + 4 + 5

= 12cm

Now, area of the triangle is given by the formula:-

\boxed{ \rm Area \: of \: the \: triangle =  \sqrt{s(s - a)(s - b)(s - c)} }

Here

• a = 3cm

• b = 4cm

• c = 5cm

\rm \:s =  \dfrac{a +b + c }{2}

\longrightarrow \rm \:s =  \dfrac{3 +4 + 5 }{2}

\longrightarrow\rm \:s =  \dfrac{12 }{2}

\longrightarrow\rm \:s =  6

Area of the triangle:-

\longrightarrow \rm    \sqrt{s(s - a)(s - b)(s - c)}

\longrightarrow \rm  \sqrt{6(6 - 3)(6 - 4)(6- 5)}

\longrightarrow \rm  =   \sqrt{6.(3).(2).(1)}

\longrightarrow \rm  =   \sqrt{6 \times  3\times 2 \times1 }

\longrightarrow \rm  =   \sqrt{36}

\longrightarrow \rm \:6 {cm}^{2}

Perimeter of triangle= 12cm

Perimeter of triangle= 12cmArea of triangle = 6cm

Hence;

\underline{\boxed{ \rm Option \: (A) \: is \: correct.}}

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