The hypotenuse of a right-angled triangle is 13 cm, and the area is 30 m2. Find the perimeter of the triangle.

1. The hypotenuse of a right-angled triangle is: C = 13 m;

2. The length of the first leg is: A m;

3. The length of the second leg is equal to: B m;

4. Area of the triangle: S = 30 sq. M;

S = 1/2 * A * B;

A = 2 * S / B = 2 * 30 / B = 60 / B m;

5. It is known that: A² + B² = C²;

(60 / B) ² + B² = 13²;

3600 + (B²) ² = 169 * B²;

(B²) ² – 169 * B² + 3600 = 0;

(B1.2) ² = 84.5 + – √ (84.52 – 3600) = 84.5 + – 59.5;

(B1) ² = 84.5 + 59.5 = 144;

B1 = √ (144) = 12 m;

A1 = 60 / B1 = 60/12 = 5 m;

(B2) ² = 84.5 – 59.5 = 25;
B2 = √ (25) = 5 m;

A2 = 60 / B2 = 60/5 = 12 m;

6. The perimeter of the triangle is: P = C + (A1 + B1) = C + (A2 + B2) = 13 + 12 + 5 = 30 m.

Answer: the perimeter of the triangle is 30 m.