Find the perimeter of a right-angled triangle if its leg and hypotenuse are 5: 13, and the second leg is 36 cm.

Let the unknown leg be equal to the mathematical expression 5a.

Then, according to the condition of the problem, it will be possible to represent using expression 13a.

Since we know from the condition of the task that the length of the known leg is 36 centimeters, it is possible to write down the equation and find out the length of the leg and hypotenuse:

36 ^ 2 + 25a ^ 2 = 169a ^ 2;

144a ^ 2 = 1296;

a ^ 2 = 9;

a1 = 3;

a2 = -3 (not suitable);

13 * 3 = 39;

5 * 3 = 15.

Let’s find the perimeter of our triangle:

36 + 15 + 39 = 90.

Answer: The perimeter is 90 centimeters.