Question

Find the area and perimeter of a trangle
Whose sides are 30cm , 40cm 50cm​

Answer 1

Answer:

120cm

Step-by-step explanation:

the perimeter of triangle=sum of three sides

=30+40+50

=120

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Answer 2

Question :-

• Find the area and perimeter of a triangle whose sides are 30 cm, 40 cm and 50 cm.

Answer :-

• Perimeter of the triangle = 120 cm.
• Area of the triangle = 600 cm².

To find :-

• The area and perimeter of a triangle whose sides are 30 cm, 40 cm and 50 cm.

Solution :-

• Before finding the area of the triangle, let's find it's perimeter!

We know that :-

• Perimeter of a triangle = Sum of all it's sides.

Here,

• The sides are 30 cm, 40 cm and 50 cm.

Therefore

$\hookrightarrow\boxed{\bf Perimeter = 30 + 40 + 50}$

$\hookrightarrow \boxed{\bf Perimeter = 120 \: cm.}$

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• Now, before finding the area of the triangle, let's find it's semi-perimeter!

We know that :-

$\underline{ \boxed{ \sf Semi-perimeter = \dfrac{a + b + c}{2} }}$

Where,

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

Here,

• First side = 30 cm.
• Second side = 40 cm.
• Third side = 50 cm.

Therefore,

$\leadsto \bf Semi-perimeter = \dfrac{30 + 40 + 50}{2}$

$\leadsto \bf Semi-perimeter = \dfrac{120}{2}$

$\leadsto \bf Semi-perimeter = 60 \: cm$

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• Now let's find the area of the triangle using Heron's formula, as we know it's semi-perimeter!

Area of a triangle is :-

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

Where,

• s = Semi-perimeter.
• a = First side.
• b = Second side.
• c = Third side.

Here,

• Semi-perimeter = 60 cm.
• First side = 30 cm.
• Second side = 40 cm.
• Third side = 50 cm.

Therefore,

$\hookrightarrow \rm A =\sqrt{60 \: (60 \!-\! 30) \: (60 \!-\! 40) \: (60\! - \!50)}$

$\hookrightarrow\rm A =\sqrt{60 \: (30) \: (20) \: (10)}$

$\hookrightarrow\rm A =\sqrt{60 \times 30 \times 20 \times 10}$

$\hookrightarrow \rm A =\sqrt{360000}$

$\hookrightarrow\rm A =600 \: {cm}^{2}$

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