The area of a right-angled triangle is 216 cm2, and the legs of a similar right-angled triangle are 3: 4.

The area of a right-angled triangle is 216 cm2, and the legs of a similar right-angled triangle are 3: 4. Find the perimeter of this triangle.

The legs of the first triangle are related to each other in the same way as the corresponding legs of a similar triangle. Therefore, the legs of the first triangle also relate to each other as 3 to 4. The area of ​​a right-angled triangle is equal to the half-product of its legs. Let’s solve the problem using the equation, where:

3x – smaller leg;

4x – larger leg;

Let’s compose and solve the equation:

1/2 * 3x * 4x = 216;

6x² = 216;

x² = 216/6;

x² = 36;

x = 6;

3x = 3 * 6 = 18 cm – smaller leg;

4x = 4 * 6 = 24 cm – larger leg.

Let’s find the hypotenuse by the Pythagorean theorem:

18² + 24² = c²;

324 + 576 = c²;

c² = 900;

c = 30 cm – hypotenuse.

Let’s find the perimeter:

P = 30 + 18 + 24 = 72 cm.

Answer: 72 cm