The sides of a triangle are in a ratio of 4: 6: 9. Find them, considering that the side equal to 24 cm

The sides of a triangle are in a ratio of 4: 6: 9. Find them, considering that the side equal to 24 cm is a) the largest b) the smallest c) average

Let x denote one fourth of the length of the shorter side of this triangle.

Then the entire length of the smaller side is 4x.

According to the condition of the problem, the lengths of the sides of a given triangle of a triangle are related as 4: 6: 9, therefore, the length of the middle side of this triangle is 6x, and the length of the longer side of this triangle is 9x.

a) The length of the longest side is 24 cm.

Consequently:

9x = 24;

x = 24/9 = 8/3 cm.

We find the other two sides:

4x = 4 * (8/3) = 32/3 cm;

6x = 6 * (8/3) = 16 cm.

Therefore, in this case, the sides of the triangle are 32/3 cm, 16 cm and 24 cm.

b) The length of the smallest side is 24 cm.

Consequently:

4x = 24;

x = 24/4 = 6 cm.

We find the other two sides:

6x = 6 * 6 = 36 cm;

9x = 9 * 6 = 54 cm.

Therefore, in this case, the sides of the triangle are 24 cm, 36 cm and 54 cm.

c) The length of the middle side is 24 cm.

Consequently:

6x = 24;

x = 24/6 = 4 cm.

We find the other two sides:

4x = 4 * 4 = 16 cm;

9x = 9 * 4 = 36 cm.

Therefore, in this case, the sides of the triangle are 16 cm, 24 cm and 36 cm.