The length of the two sides of a right-angled triangle containing the right angle differ by 2 cm. If thearea of the triangle is 24 cm2, then find the perimeter of the triangle

Let's denote the length of the shorter side of the right-angled triangle as "a" (in cm). Then, the length of the longer side that contains the right angle would be "a + 2" (in cm).

The area of a right-angled triangle is given by the formula: 1/2 * base * height. In this case, the base and height are the two sides containing the right angle. So, we can write the equation for the area as follows:

24 = 1/2 * a * (a + 2)

Solving this equation for "a" will give us the lengths of the two sides containing the right angle. Then, we can use the Pythagorean theorem (a^2 + b^2 = c^2) to find the length of the hypotenuse (c), where "a" and "b" are the lengths of the two sides containing the right angle.

Finally, the perimeter of the triangle is the sum of the lengths of all its sides. So, we add up the lengths of the two sides containing the right angle and the hypotenuse to find the perimeter.