Question

4. A right triangle has legs with lengths of 6 feet and 9 feet. The hypotenuse of the triangle, in feet,

is between:
A. 4 and 5
B. 6 and 9
C. 9 and 10
D. 10 and 11
E. 11 and 13

Answer 1

D. 10 and 11

Explanation:

This problem would use pythagorean theorem because we're finding the hypotenuse of a right triangle. This is its standard equation:

`a {}^(2) + {b}^(2) = {c}^(2)`

The legs represent
`a` and
`b` respectively, and
`c` represents the hypotenuse. After plugging in the legs' respective values, the equation looks like this:

`6^(2) + {9}^(2) = {c}^(2) →36 + 81 = {c}^(2) →117 = c^(2)`

To isolate
`c`, you would find the square root of
`117`. In this case, we're just finding which integers
`√(117)` is between.
`√(100)(=10)` is the closest integer value below
`√(117)` and
`√(121)(=11)` is the closest integer value above
`√(117)`. So the answer is D. 10 and 11.

Answer 2

To solve for the hypotenuse or the longest side of the triangle, we can simply use the Pythagorean Theorum.

C^2 = A^2 + B^2
C^2 = (6)^2 + (9)^2
C^2 = 36 + 81
C^2 = 117
C = square root of 117
C = About 10.81 feet

So, in conclusion, the hypotenuse or the longest side of the triangle in feet is: D. Between 10 feet and 11 feet.