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

September 29, 2021 | education

| **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.