If one of the sides of the triangle is 3 cm less than the other, the height divides the third side into segments

If one of the sides of the triangle is 3 cm less than the other, the height divides the third side into segments of 5 cm and 10 cm, then the perimeter of the triangle is ..

We take for x one of the sides of the triangle, then:

x + 3 is the other side;

√ (x ^ 2 – 5 ^ 2) – height;

√ ((x + 3) ^ 2 – 8 ^ 2) – also height.

We get the equation:

x ^ 2 – 25 = (x + 3) ^ 2 – 64;

x ^ 2 – x ^ 2 – 6x – 9 = -64 + 25;

6x + 9 = 39;

x = 5.

Then the second side is equal to:

5 + 3 = 8 cm.

And the third:

5 + 8 = 13.

The perimeter is:

5 + 8 + 13 = 26 cm.

Answer: the desired perimeter of a given triangle is 26 cm.