Answer:
1) 5, 7, 8
2) 10, 24, 26
Step-by-step 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.
