Question

What are the lengths of the sides of triangle ABC, given that the ratio of the sides is 3:4:6, and the perimeter of triangle MNK (whose vertices are the midpoints of ABC) is 13 units?

A) AB = 39/8 units, BC = 52/8 units, AC = 7/8 units
B) AB = 3 units, BC = 4 units, AC = 6 units
C) AB = 6 units, BC = 8 units, AC = 12 units
D) AB = 13/8 units, BC = 13/2 units, AC =13/4 units

Answer 1

The lengths of the sides of triangle ABC, given the ratio of 3:4:6 and the perimeter of triangle MNK as 13 units, are AB = 3 units, BC = 4 units, and AC = 6 units.

Step-by-step explanation:

To find the lengths of the sides of triangle ABC, we need to use the given ratio of 3:4:6. Let's assume the common ratio as x. The lengths of the sides of triangle ABC would be 3x, 4x, and 6x units.

Since the midpoints of ABC form triangle MNK, whose perimeter is given as 13 units, we can set up the equation: 3x + 4x + 6x = 13.

Simplifying the equation, we get 13x = 13, which implies x = 1. Therefore, the lengths of the sides of triangle ABC are AB = 3 units, BC = 4 units, and AC = 6 units.