The perimeter of the ABC triangle is 44 cm. The AB side is half the size of the DC

| June 16, 2021 | education

The perimeter of the ABC triangle is 44 cm. The AB side is half the size of the DC side and 4 cm less than the AC side. Find the lengths of all sides of the triangle.

According to the condition of the problem, the perimeter of the triangle abc is 44 cm, therefore, the following relation holds:
| ab | + | bc | + | ac | = 44.
It is also known that ab is half the size of the bc side and 4 cm smaller than the ac side, therefore, the following relations hold:
| bc | = 2 * | ab |;
| ac | = | ab | + 4.
We solve the resulting system of equations. Substituting into the first equation the values ​​for | bc | and | ac | from the second and third equations, we obtain:
| ab | + 2 * | ab | + | ab | + 4 = 44.
We solve the resulting equation:
4 * | ab | + 4 = 44;
4 * | ab | = 44 – 4;
4 * | ab | = 40;
| ab | = 40/4;
| ab | = 10 cm.
Knowing | ab |, we find | bc | and | ac |:
| bc | = 2 * | ab | = 2 * 10 = 20 cm;
| ac | = | ab | + 4 = 10 + 4 = 14 si.

Answer: side ab is 10 cm, side bc is 20 cm, side ac is 14 cm.



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