In right triangle ABC, the lengths of the two legs perpendicular to each other are 9 and 1… — GRE General Test

In right triangle $ABC$ , the lengths of the two legs perpendicular to each other are $9$ and $12$ . What is the perimeter of triangle $ABC$ ?

The perimeter of triangle

ABC

36

Using the Pythagorean theorem, the hypotenuse length is

\sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15

. Summing the two legs (

9

and

12

) with the hypotenuse (

15

) gives a total perimeter of

36

Calculate the length of the hypotenuse using the Pythagorean theorem.

Hypotenuse

c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15

For any right triangle with legs

a

and

b

and hypotenuse

c

a^2 + b^2 = c^2

holds.

Sum the lengths of all three sides to find the perimeter.

Perimeter

= 9 + 12 + 15 = 36

The perimeter of a polygon is the total distance around its outer boundary.

Pythagorean Theorem (

a^2 + b^2 = c^2

) and Perimeter of Triangles

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