Question

an isosceles tringle has perimeter 30cm and each of the equal sides is 12 cm .find the area of the triangle.​

Answer 1

Answer:

The base is 8 cm.

Using herons formula, S = 16.

Area = √ [ 16 • 4 • 4 • 8 ] = 64√2 cm sq.

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Answer 2

First,let the third side be x.

It is given that the length of the equal sides is 12 cm and it's perimeter is 30 cm.

So,$30=12+12+x$

$⇒ 30 = 24 + x$

$⇒24 + x = 30$

$⇒ x= 30 - 24$

$⇒ x = 6$

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

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

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)} \: {cm}^{2}$

$= \sqrt{15 \times 3 \times 3 \times 9} \: {cm}^{2}$

$= 9 \sqrt{15} \: {cm}^{2}$