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प्रश्न
If a triangle having sides 8 cm, 15 cm and 17 cm, then state whether given triangle is right angled triangle or not
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उत्तर
The sides of the triangle are 8 cm, 15 cm, and 17 cm.
The longest side of the triangle is 17 cm.
∴ (17)2 = 289
Now, sum of the squares of the remaining sides is,
(8)2 + (15)2 = 64 + 225 = 289
∴ (17)2 = (8)2 + (15)2
∴ Square of the longest side is equal to the sum of the squares of the remaining two sides.
∴ The given sides will form a right-angled triangle. ......[Converse of Pythagoras theorem]
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Choose the correct alternative:
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*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)
Activity: In ∆LMN, l = 5, m = 13, n = `square`
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∴ l2 + n2 = 25 + 144 = `square`
∴ `square` + l2 = m2
∴By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
