The sides of a triangle are 2: 4: 5. Find the perimeter of a triangle similar to this one if the sum

The sides of a triangle are 2: 4: 5. Find the perimeter of a triangle similar to this one if the sum of its largest and smallest sides is 21cm.

Triangles ABC And A1B1C1 are similar. Let us assume that the sides ∆ABS are equal:

AB = 2 cm;

BC = 4 cm;

AC = 5 cm.

Since the sum of the largest and smallest sides ∆А1В1С1 is equal to 21 cm, then you need to find the sum of the corresponding sides ∆ABS. Such parties are the parties AB and AC:

AB + AC = 2 + 5 = 7 cm.

Now you can find the coefficient of similarity for these sides:

k = (A1B1 + A1C1) / (AB + AC);

k = 21/7 = 3.

Now we find the sides of the triangle ∆А1В1С1:

A1B1 = AB · k;

В1С1 = ВС · k;

A1C1 = AC · k;

A1B1 = 2 3 = 6 cm;

B1C1 = 4 3 = 12 cm;

A1C1 = 5 3 = 15 cm.

Let’s find the perimeter of the triangle ∆А1В1С1:

PA1B1C1 = A1B1 + B1C1 + A1C1;

PA1B1C1 = 6 + 12 + 15 = 33 cm.

Answer: the perimeter of the triangle ∆А1В1С1 is 33 cm.