In a right-angled triangle, the hypotenuse refers to the leg as 5: 3. Find the perimeter of the triangle if the second leg is 12cm.

univerkov | February 5, 2021 | education

1. AC = 12 cm – leg of a right-angled triangle ABC. ∠А = 90 °. BC: AB = 5: 3. R – perimeter

triangle.

2. According to the condition of the problem BC: AB = 5: 3. Therefore, AB = 3BC / 5.

3. We calculate the length of the second leg (AB), using the Pythagorean theorem:

BC² = AB² + AC². Substitute in this expression 3BC / 5 instead of AB.

ВС² = (3ВS / 5) ² + 12².

BC² = 9BC² / 25 + 144.

25BC² – 9BC² = 144 x 25.

16BC² = 144 x 25.

BC² = 9 x 25.

BC = √9 x 25 = 3 x 5 = 15 cm.

AB = 3BC / 5 = 3 x 15: 5 = 9 cm.

4.R = 15 + 12 + 9 = 36 cm.

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