the sides of a triangle are in the ratio 12 17 25 and its semi perimeter is 270 cm. find it's area
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the sides of a triangle are in the ratio 12 17 25 and its semi perimeter is 270 cm. find it's area
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Ratio of sides of ∆ is 12:17:25.
Semi perimeter of ∆ is 270 cm.
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☯ Let sides of ∆ be 12x, 17x and 25x.
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Here,
Semi - Perimeter of ∆ is 270 cm
Therefore,
Perimeter of ∆ is 2 × 270 = 540 cm
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We know that,
☯ Perimeter of ∆ = sum of all sides
➯ 540 = 12x + 17x + 25x
➯ 540 = 54x
➯ x = 10
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Therefore,
Measure of all sides of ∆ is,
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⋆ Reference of image is shown in diagram
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We know that,
☯ Area of ∆ is can be find using Heron's Formula,
where,
s = Semi - perimeter
➯ s = 270 cm
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★ Now, Putting values,
Area of triangle is 9000 cm².
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