Question

15. An isosceles triangle has perimeter 84 cm and
each of the equal sides is 30 cm. Find the
area of the triangle.​

Answer 1

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A≈336.75cm²

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Answer 2

First,let the third side be x.

It is given that the length of the equal sides is 30 cm and it's perimeter is 84 cm.

So,84=30+30+x

⇒ 84 = 60 + x

⇒60 + x = 84

⇒ x= 84 - 60

⇒ x = 24

So,the length of the third side is 24 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 84/2 cm =42 cm

By using Heron's Formula,

Area of the triangle,

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

$= \sqrt{42(42 - 30)(42- 30)(42 - 24)} \: {cm}^{2}$

$= \sqrt{42 \times 12\times 12\times 18} \: {cm}^{2}$

$= 329.94545 \: {cm}^{2}$