Question

The ratio of the lengths of the sides of triangle abc is 2:3:4. points m, n, and k are the midpoints of the sides. the perimeter of triangle mnk equals 7.2

Answer 1

The lengths of the sides of triangle ABC are AB = 3.2 inches, BC = 4.8 inches, and AC = 6.4 inches.

Explanation:

To find the lengths of the sides of triangle ABC, we can use the fact that the midpoints of the sides of a triangle divide each side into segments that are proportional to the entire side.

Let's denote the lengths of the sides of triangle ABC as 2x, 3x, and 4x.

Then, the midpoints of the sides create a smaller triangle mnk with sides that are half the length of the corresponding sides in triangle ABC.

The perimeter of triangle mnk is given as 7.2 inches, and since the sides of mnk are half the corresponding sides of ABC, we can set up the following equation:

2x/2 + 3x/2 + 4x/2 = 7.2

x + 1.5x + 2x = 7.2

4.5x = 7.2

x = 7.2 / 4.5

x = 1.6

So, the lengths of the sides of triangle ABC are:

AB = 2x = 2 * 1.6 = 3.2 in

BC = 3x = 3 * 1.6 = 4.8 in

AC = 4x = 4 * 1.6 = 6.4 in

Therefore, the length of the sides of triangle ABC are:

AB = 3.2 inches, BC = 4.8 inches, and AC = 6.4 inches.