Read the scenario below and provide the missing numeric value.

Answer:An architect is designing a courtyard in the shape of a right triangle. The two perpendicular walkways that form the right angle measure

9

meters and

12

meters in length. The length of the diagonal path connecting their endpoints is 【15】 meters.

The diagonal path is

15

meters long.

By applying the Pythagorean theorem (

a^2 + b^2 = c^2

) with legs of

9

and

12

, we calculate

9^2 + 12^2 = 81 + 144 = 225

. The square root of

225

15

, which is the exact length of the diagonal path.

Identify the known sides of the right triangle.

The two perpendicular walkways represent the legs of the triangle (

a

and

b

), measuring

9

and

12

To accurately apply the Pythagorean theorem, the given measurements must be identified as either legs or the hypotenuse.

Apply the Pythagorean theorem (

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

The theorem is used to find the hypotenuse (

c

) when the lengths of both legs are known.

Square the lengths of both legs.

81 + 144 = c^2

Following mathematical order of operations by evaluating the exponents first.

Add the squared values and solve for

c

225 = c^2

, which means

c = \sqrt{225} = 15

Taking the square root of the sum yields the final straight-line length of the hypotenuse.

Using the Pythagorean theorem (

a^2 + b^2 = c^2

) to calculate the length of the hypotenuse when both legs are known.

Question