Two sides of a triangle are 7 cm and 10 cm, and the third side, x cm, is the longest side. For how many integer values of x is the triangle obtuse-angled?

Question

Accepted Answer

4. x must be longer than 10 and less than 7 + 10 = 17. For an obtuse angle opposite x we need x^2 > 7^2 + 10^2 = 149, so x ≥ 13. The values are 13, 14, 15 and 16: four in all.

Two sides of a triangle are 7 cm and 10 cm, and the third side, $x$ cm, is the longest side. For how many integer values of $x$ is the triangle obtuse-angled?

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