Determine the missing side length based on the geometric properties of a right triangle.

Answer:In a right triangle, the two shorter sides (legs) measure

9

cm and

12

cm. According to the Pythagorean theorem, the length of the hypotenuse is 【15】 cm.

By applying the Pythagorean theorem (

a^2 + b^2 = c^2

) to a right triangle with legs of

9

and

12

, we square both numbers to get

81

and

144

. Their sum is

225

. The hypotenuse is the square root of

225

, which is

15

Identify the known sides of the right triangle.

The legs (let's call them

a

and

b

) measure

9

cm and

12

cm.

The Pythagorean theorem requires knowing the lengths of two sides to find the third.

Set up the Pythagorean theorem equation.

a^2 + b^2 = c^2

, which becomes

9^2 + 12^2 = c^2

This formula relates the squares of the legs to the square of the hypotenuse (

c

Square the lengths of the two legs and add them together.

81 + 144 = 225

This calculation determines the value of

c^2

Take the square root of the sum to find the hypotenuse.

\sqrt{225} = 15

Since

c^2 = 225

, taking the square root gives the actual length of the hypotenuse (

c

Pythagorean Theorem

Question