Question

The ratio of the lengths of the sides of△ ABC is 2:3:4. points M, N, and K are the midpoints of the sides. the perimeter of AMNK equals 7.2 in. find the length of the sides of △ABC?

A)2.4 inches, 3.6 inches, 4.8 inches
B) 1.2 inches, 1.8 inches, 2.4inches
C)4.8 inches, 7.2inches, 9.6inches
D)3.6inches, 5.4inches, 7.2inches

Answer 1

The lengths of the sides of triangle ABC are 1.6 inches, 2.4 inches, and 3.2 inches.

Step-by-step explanation:

First, we need to determine the lengths of the sides of triangle ABC. Let's assign a scale factor of 2 to the shortest side, so the lengths of the sides are 2n, 3n, and 4n. The perimeter of AMNK is the sum of the lengths of the sides of triangle ABC. We know that the perimeter of AMNK is 7.2 inches. So, we can set up the equation 2n + 3n + 4n = 7.2 and solve for n.

2n + 3n + 4n = 7.2
9n = 7.2
n = 0.8

Now, we can find the lengths of the sides of triangle ABC:
Side AB = 2n = 2(0.8) = 1.6 inches
Side BC = 3n = 3(0.8) = 2.4 inches
Side AC = 4n = 4(0.8) = 3.2 inches

Therefore, the lengths of the sides of triangle ABC are 1.6 inches, 2.4 inches, and 3.2 inches, which matches option D: 3.6 inches, 5.4 inches, 7.2 inches.