The sides of the triangle are in the ratio 2: 4: 5. Find the sides of a similar triangle

| September 22, 2021 | education

The sides of the triangle are in the ratio 2: 4: 5. Find the sides of a similar triangle, in which the difference between the largest and smallest sides is exactly 12cm.

Suppose that the dimensions of the sides of the first triangle are equal to AB = 2 cm, BC = 4 cm; AC = 5 cm.

Let’s find the difference between the larger and smaller sides of the first triangle:

AC – AB = 5 – 2 = 3 cm.

Now we can find the coefficient of similarity by the difference in the lengths of these sides, since in such triangles the corresponding sides are proportional:

k = (A1C1 – A1B1) / (AC / AB);

k = 12/3 = 4.

Now we can find the sides of the triangle A1B1C1:

A1B1 = AB · k;

A1B1 = 2 4 = 8 cm;

В1С1 = ВС · k;

B1C1 = 4 4 = 16 cm;

A1C1 = AC · k;

A1C1 = 5 4 = 20 cm.

Answer: the sides of triangle A1B1C1 are 8 cm, 16 cm, 20 cm.



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