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  • Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find the area of the triangle.

Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find the area of the triangle.

Answers (1)

Let the sides of the triangle be 12x cm 17x cm and 25x cm. 

Perimeter of the triangle = 540 cm 

∴ 12x + 17x + 25x = 540 

⇒ 54 x = 540 

⇒ x = 540/ 54 = 10 

∴ Sides of the triangle are (12 × 10) cm, (17 × 10) cm and (25 × 10) cm i.e., 120 cm, 170 cm and 250 cm. 

Now, suppose a = 120cm, b = 170 cm, c = 250 cm,  ∴ s = (a +b + c)/ 2 =  540/ 2 cm = 270 cm

Area of the triangle

\begin{array}{l} =\sqrt{s(s-a)(s-b)(s-c)} \\ \\ =\sqrt{270(270-120)(270-170)(270-250)} \mathrm{cm}^{2} \\ \\ =\sqrt{270 \times 150 \times 100 \times 20} \mathrm{cm}^{2}=9000 \mathrm \ {cm}^{2} \end{array}

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lovekush

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