Find the perimeter of a right-angled triangle if its legs are 3: 4, and the hypotenuse is 25 dm.
| September 20, 2021 | education
1. A, B, C – the vertices of the triangle. Angle A = 90 degrees. P is the perimeter.
2. By the condition of the problem AB: AC = 3: 4. Therefore, AB = 3AC / 4.
3. AC² + AB² = BC² (by the Pythagorean theorem).
4. Substitute in this expression 3AC / 4 instead of AB:
AC² + (3AC / 4) ² = 625.
AC² + 9AC² / 16 = 625.
25АС² / 16 = 625.
AC² = 16 x 25.
AC = √16 x 25 = 4 x 5 = 20 decimeters.
AB = 3AC / 4 = 3 x 20: 4 = 15 decimeters.
5.R = 15 + 20 + 25 = 60 decimeters.
Answer: P is equal to 60 decimeters.
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