Question

length of side of a triangle are 10cm ,18cm and primeter is 42 cm .find its area.​

Answer 1

Given

Length of two sides of the triangles are 10 cm and 18 cm respectively.

Perimeter of Triangle ⇒ 42 cm

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To Find

The area of the given triangle.

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Solution

We are only given with two sides of the triangle so we have to find the third side.

Side 1 ⇒ 10 cm

Side 2 ⇒ 18 cm

Side 3 ⇒ x

Perimeter of Triangle ⇒ Side 1 + Side 2 + Side 3

Perimeter of Given Triangle ⇒ 42 cm

Let's consider side C as 'x' and solve this equation ⇒ 10 + 18 + x = 42

Step 1: Simplify the equation.

10 + 18 + x = 42

28 + x = 42

Step 2: Subtract 28 from both sides of the equation.

28 + x - 28 = 42 - 28

x = 14

∴ The third side measures 14 cm.

Since we have all three sides of the triangle and also the perimeter now we can proceed for finding the area of the triangle using the Heron Law.

Heron Law ⇒ $\sqrt{s(s-a)(s-b)(s-c)}$

Here the value of 's' is half of the perimeter. For the following question 's' would be 42÷2 = 21

Let's find the area using heron's law now.

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

$\sqrt{21(21-10)(21-18)(21-14)}$

$\sqrt{21(11)(3)(7)}$

$\sqrt{21\times 11\times 21}$

$(\sqrt{21})^{2}\times \sqrt{11}$

$21\sqrt{11}$

∴ The area of the given triangle is 21√11 cm²

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