The sides of the triangle are 11 cm, 15 cm and 16 cm. Find the projections

The sides of the triangle are 11 cm, 15 cm and 16 cm. Find the projections of the smallest and largest sides of the triangle onto the middle side.

In order to find the sides similar to a given triangle, if its perimeter is known, we start by introducing the similarity coefficient k and writing the lengths of the sides as 5k, 3k and 7k.

To compose the equation, we apply the formula for calculating the perimeter of a triangle:

P = a + b + c,

We substitute the values in the formula and solve the resulting equation:

3k + 5k + 7k = 105;

15k = 105;

k = 105: 15;

k = 7.

We get the values of the lengths of the sides of a triangle similar to the given one:

3 * 7 = 21 cm, 5 * 7 = 35 cm, 7 * 7 = 49 cm.