Question

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

Answer 1

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.

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

Answer 2

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;

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