Given below are the sides of a triangle. In which cases are the triangles right angled?

(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

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Solution

We know that in a right triangle, the hypotenuse is the longest side.

(i)

17² = 189 and 8² + 15² = 289

∴ 17² = 8² + 15²

Thus, 8, 15 and 17 are the sides of a right triangle.

(ii)

14² = 196 and 9² + 10² = 181

∴ 14² ≠ 9² + 10²

Thus, 9, 10 and 14 are not the sides of a right triangle.

(iii)

25² = 625 and 7² + 24² = 625

∴ 25² = 7² + 24²

Thus, 7, 24 and 25 are the sides of a right triangle.

Hence, in cases (i) and (ii), the triangles are right triangles.

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Given below are the sides of a triangle. In which cases are the triangles right angled? (i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25

Given below are the sides of a triangle. In which cases are the triangles right angled?

(i) 8, 15, 17 (ii) 9, 10, 14 (iii) 7, 24, 25