Answer:
36 units
Explanation:
You want to know the perimeter of the right triangle with leg lengths 9 units and 12 units.
Perimeter
The perimeter of the triangle is the sum of the lengths of its sides. We can count squares to find the lengths of the horizontal and vertical legs. The length of the hypotenuse can be found using the Pythagorean theorem:
c² = a² +b²
c² = 9² +12² = 81 +144 = 225
c = √225 = 15 . . . . length of the hypotenuse
Then the perimeter is ...
P = a +b +c = 9 +12 +15 = 36 . . . units
The perimeter of the triangle is 36 units.
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Additional comment
The leg lengths have the ratio 9:12 = 3:4, telling you this is a 3:4:5 right triangle. This means you know the side lengths are 3:4:5 = 9:12:15, and their sum is 9+12+15 = 36.
It is handy to memorize a few of the Pythagorean triples that often show up in algebra, trig, and geometry problems: {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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