Question

find the area of a triangle two sifes of which are 18 and 10 and the perimeter is 42 cm..using herons formula ​

Answer 1

Answer:

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Answer 2

Answer:

Area of the triangle is 69.65 cm².

Step-by-step explanation:

Given :-

• Two sides of the triangle are 18 cm and 10 cm.
• Perimeter of the triangle is 42 cm.

To find :-

• Area of the triangle.

Solution :-

Let the third side of the triangle be x cm.

★Formula used :

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

• a = 1st side
• b = 2nd side
• c = 3rd side

Perimeter of the triangle,

= (18+10+x ) cm

= (28+x) cm

According to the question,

28+x = 42

→ x = 42-28

→ x = 14

Third side of the triangle is 14 cm.

★ Formula used :

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

• s = semi perimeter

Then,

Semi perimeter of the triangle

= Perimeter/2

= 42/2 cm

= 21 cm

Area of the triangle,

$\to \sf \: \sqrt{21(21 - 18)(21 - 10)(21 - 14)} \: {cm}^{2} \\ \\ \to \sf \: \sqrt{21 \times 3 \times 11 \times 7} \: {cm}^{2} \\ \\ \to \sf \: \sqrt{4851} \: {cm}^{2} \\ \\ \to \sf \: 69.65 \: {cm}^{2}$

Therefore, area of the triangle is 69.65 cm².