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What triangle has 15in each and the third side measures 10in?

Updated: 8/19/2019
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Superstar2011

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13y ago

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An isosceles triangle.

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13y ago
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Q: What triangle has 15in each and the third side measures 10in?
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What could not be the lengths of the sides of a right triangle 9ft 12ft 15ft or 4cm 7.5cm 8.5cm or 5in 10in 15in or 1.5m 2m 2.5m?

5" by 10" by 15" cannot be a right angled triangle because the square of the hypotenuse (longest side) must be equal to the sum of the squares of the other two sides.Proof:152 = 22552 + 102 = 25 + 100 = 125225 is not equal to 125 so the triangle is not a right angled triangle.All the others are right-angled triangles:92 + 122 = 152 [81 + 144 = 225]42 + 7.52 = 8.52 [16 + 56.25 = 72.25]1.52 + 22 = 2.52 [2.25 + 4 = 6.25]Answer9ft, 12ft, 15ft9² + 12² = 81 + 144= 225= 15²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.4cm, 7.5cm, 8.5cm4² + 7.5² = 16 + 56.25= 72.25= 8.5²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.5in, 10in, 15inThis one doesn't obey the triangle inequality, so it isn't a triangle at all. Anything that isn't a triangle isn't a right-angled triangle, and therefore we don't need to check it against Pythagoras' Theorem. But just to be thorough:5² + 10² = 25 + 100= 12515² = 225≠ 125Which disagrees with Pythagoras' Theorem, so this is not a right-angled triangle.1.5m, 2m, 2.5m1.5² + 2² = 2.25 + 4= 6.25= 2.5²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.


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