Question

Which length could be the lengths of the sides of a triangle?
A. 6 cm, 10 cm, 9 cm
B. 8 cm, 4 cm, 2 cm
C. • 7 cm, 7 cm, 34 cm
D. • 10 cm, 25 cm, 15 cm

Answer 1

The lengths of the sides of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check each option:

A. 6 cm, 10 cm, 9 cm. This satisfies the triangle inequality theorem because 6 + 9 > 10, 6 + 10 > 9, and 9 + 10 > 6. This could be the lengths of the sides of a triangle.

B. 8 cm, 4 cm, 2 cm. This does not satisfy the triangle inequality theorem because 4 + 2 is not greater than 8. This cannot be the lengths of the sides of a triangle.

C. 7 cm, 7 cm, 34 cm. This does not satisfy the triangle inequality theorem because 7 + 7 is not greater than 34. This cannot be the lengths of the sides of a triangle.

D. 10 cm, 25 cm, 15 cm. This satisfies the triangle inequality theorem because 10 + 15 > 25, 10 + 25 > 15, and 15 + 25 > 10. This could be the lengths of the sides of a triangle.

Therefore, the lengths of the sides of a triangle are A. 6 cm, 10 cm, 9 cm and D. 10 cm, 25 cm, 15 cm.