What is the perimeter of this triangle ?

36 units

Step-by-step explanation:

The two legs of this right triangle are 9 and 12. In order to find the length of the hypotenuse, you must plug in the 9 and 12 to the Pythagorean theorem:

a^2 + b^2 = c^2, where a and b are legs and c is the hypotenuse

If you plug in the values 9 and 12, you get:

9^2 + 12^2 = c^2

= 81 + 144 = c^2

= 225 = c^2

= 15 = c

This means that the hypotenuse is 15 units long. Now, you just need to add all the sides to get:

9 + 12 + 15

= 36 units

(Also as a fun fact, a Pythagorean Triple is when the three sides of a right triangle are integers. It is good to memorize a few of these, like 3-4-5, 5-12-13, 7-24-25 and 8-15-17. The largest side value is always the hypotenuse, and if you multiply all the sides by a scale factor, you can get other triples. If you knew the 3-4-5 triple, you might have noticed that 9 and 12 are 3 times each of the legs 3 and 4. From that information, you could just multiply the 5 by 3 to get 15 for the hypotenuse of this triangle, which might've made this problem a little easier)