Question

one of the equal sides of an isosceles triangle is 13cm and it's perimeter is 50 CM. find the area of the triangle

Answer 1

We know that the length of two sides in isosceles triangle is equal. Given that one of the equal line is of 13 cm, so length of other side should also be 13 cm.

Now,

Length of equal to sides = 13 cm each

Perimeter of triangle = 50 cm

⇒ Perimeter of triangle = sum of equal sides + base side ( 3rd side )

⇒ 50 cm = 13 cm + 13 cm + 3rd side

⇒ 50 cm = 26 cm + 3rd side

⇒ 50 cm - 26 cm = 3rd side

⇒ 24 cm = 3rd side

∴Length of third side is 24 cm.

Then,

Semi perimeter of the triangle = 1 / 2 x perimeter of the triangle

Semi perimeter of the triangle = 1 / 2 x 50 cm

Semi perimeter of the triangle = 25 cm

By Heron's formula

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

therefore, applying heron's formula for the area of the triangle.

$\implies Area = \sqrt{25(25-13)(25-13)(25-24)\text{cm}^4}\\\\\implies Area = \sqrt{25\times 12\times \times 12\times 1\text{cm}^4} \\\\\implies Area = \sqrt{5^2 \times 12^2 }\\\\\implies Area = 5 \times 12 cm^2\\\\\implies Area = 60 cm^2$

Therefore, area of the triangle is 60 cm^2.

Answer 2

Equal side is 13 cm
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As we know isosceles triangle have equal side
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Perimeter=Sum of two equal side+ Third side
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50=26+Third side
50-26=Third side
24=Third side

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s=Perimeter/2=>50/2=25cm
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Area=√s(s-a)(s-b)(s-c)
=√25(25-13)(25-13)(25-24)
=√25×12×12×1
=√3600cm⁴
=60cm²