Math, asked by amishubhi1365, 7 months ago

The lengths of the sides of a triangle are in the ratio 3:4:5 and it's perimeter is 144cm find it's area

Answers

Answered by MaIeficent
8

Step-by-step explanation:

The ratio of the sides of a triangle = 3 : 4 : 5

Let the common ratio of the sides be x

Therefore, the sides are 3x, 4x and 5x

As we know that:-

Perimeter of triangle = Sum of its sides

⇢3x + 4x + 5x = 144

⇢12x = 144

⇢x = \dfrac{144}{12} = 12

The sides are:-

⇢ a = 3x = 3 × 12 = 36cm

⇢b = 4x = 4 × 12 = 48cm

⇢c = 5x = 5 × 12 = 60cm

Semi - perimeter (s) = \dfrac{144}{2} = 72

\rm Area\: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)}

 = \rm\sqrt{72(72 - 36)(72 - 48)(72 - 60)}

 = \rm\sqrt{72 \times 36 \times 24 \times 12}

 = \rm\sqrt{746496}

 = \rm864

   \underline{ \boxed{\rm \therefore \: Area \: of \: the \: triangle  = 864 {cm}^{2}}}

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