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Question
If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
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Solution
Let, the sides of the triangle be, x: `sqrt2`x and x.
AB2 + BC2 = x2 +x2 = 2x2
AC2 = `(sqrt2 x)^2` = 2x2
AB2 + BC2 = AC2
Conversely, if in any triangle, the square on the largest side of the triangle is equal to the sum of the squares on remaining two sides, then the triangle is a right-angled triangle and the angle opposite to the largest side is a right-angle.
Therefore, Δ ABC is a right-angled triangle.
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