Question

Which set of numbers can represent the side lengths, in inches, of an acute triangle? 4, 5, 7 5, 7, 8 6, 7, 10 7, 9, 12 Which set of numbers can represent the side lengths, in centimeters, of a right triangle? 8, 12, 15 10, 24, 26 12, 20, 25 15, 18, 20

Answer 1

1) 5, 7, 8

2) 10, 24, 26

Explanation:

1) For an acute triangle, the square of the longest side is less than the sum of the square of the two smaller sides.

a) 4² + 5² = 16 + 25 = 41

7² = 49 > 4² + 5². Therefore the triangle is not acute

b) 5² + 7² = 25 + 49 = 74

8² = 64 < 5² + 7². Therefore the triangle is acute

c) 6² + 7² = 36 + 49 = 85

10² = 100 > 6² + 7². Therefore the triangle is not acute

d) 7² + 9² = 49 + 81 = 130

12² = 144 > 7² + 9². Therefore the triangle is not acute

2) For a right angled triangle, the square of the longest side is equal to the sum of the square of the two smaller sides.

a) 8² + 12² = 64 + 144 = 208

15² = 225 > 8² + 12². Therefore the triangle is not a right triangle.

b) 10² + 24² = 100 + 576 = 676

26² = 676 = 10² + 24². Therefore the triangle is a right triangle.

c) 20² + 12² = 400 + 144 = 544

25² = 625 > 20² + 12². Therefore the triangle is not a right triangle.

d) 15² + 18² = 225 + 324 = 549

20² = 400 < 15² + 18². Therefore the triangle is not a right triangle.