Two sides of a triangle = 17cm and 25cm. The height divides the third side into segments

| March 3, 2021 | education

Two sides of a triangle = 17cm and 25cm. The height divides the third side into segments, the difference of which is 12cm. Find the perimeter of the triangle.

1. Vertices of the triangle A, B, C. ВK – height. AB = 17 cm. BC = 25 cm. СK – AK = 12 cm.

2. ВK² = AB² – AK² (by the Pythagorean theorem).

BK² = ВС² – CK² (by the Pythagorean theorem).
…
AB² – AK² = BC² – СK².

2. We take the length of the segment AK for x (cm). The length of the segment СK = (x + 12) cm.

289 – x² = 625 – (x + 12) ²;

289 – x² = 625 – x² – 24x – 144;

24x = 192;

x = 8.

AK = 8 cm.

СK = 8 + 12 = 20 cm.

3. Side length AC = AK + СK = 8 + 20 = 28 cm.

4. Calculate the total length of all sides (perimeter) of a given triangle:

17 + 25 + 28 = 70 cm.

Answer: the perimeter of the given triangle is 70 cm.



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