The sides of the triangle are proportional to the numbers 2,5,4. Find the middle side

The sides of the triangle are proportional to the numbers 2,5,4. Find the middle side of a similar triangle with the smaller side 22 cm.

Let us denote by a half the length of the smaller of the sides of a similar triangle.

Then the length of this smaller side should be 2a cm.

Since the ratio of the lengths of the sides of such a triangle is two to five to four, then the ratio of the lengths of the sides will be the same for the desired triangle.

Therefore, the lengths of the other two sides should be 5a cm and 4a cm.

Since the length of the shorter side of the desired triangle is 22 cm, we can make the following equation:

2a = 22,

solving which, we get:

a = 22/2 = 11 cm.

Find the length of the middle side:

4a = 2 * 11 = 44 cm.

Answer: 44 cm.