Question

FIll in the blanks!

Determine the length of the hypotenuse of this right triangle.
Pythagorean theorem: a^(2) + b^(2) = _

Traingle : c, 8 cm, 5 cm
a^(2) + b^(2) = c^(2)
_^(2) + 5^(2) = c^(2)
64 + _ = c^(2)
_ = c^(2)
\sqrt(89) = \sqrt(c^(2)
\sqrt(_)cm = c

Answer 1

To fill in the blanks using the Pythagorean theorem for the right triangle with sides of length 8 cm and 5 cm, let's follow the problem step by step.

1. Pythagorean theorem: \(a^2 + b^2 = c^2\)

2. Triangle: \(c, 8 \text{ cm}, 5 \text{ cm}\)
\[
8^2 + 5^2 = c^2
\]

3. Calculate the squares:
\[
8^2 = 64
\]
\[
5^2 = 25
\]

4. Substitute into the equation:
\[
64 + 25 = c^2
\]

5. Add the results:
\[
64 + 25 = 89
\]
Therefore, \(c^2 = 89\).

6. To find \(c\):
\[
c = \sqrt{89}
\]

So, filling in the blanks:

- The Pythagorean theorem: \(a^2 + b^2 = c^2\)
- \(8^2 + 5^2 = c^2\)
- \(64 + 25 = c^2\)
- \(25 = c^2\)
- \(\sqrt{89} = \sqrt{c^2}\)
- \(\sqrt{89} \text{ cm} = c\)

Thus, the complete filled-in statement would be:

1. \(c^2\)
2. \(25\)
3. \(89\)