Question

Use the given information to match the answers.

ABC is a right triangle.

1. 2√13
2. √5
3. 3√3

1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =

Answer 1

Hey there!

Solve them by using

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


1.

`{a}^(2) + {2}^(2) = {3}^(2) \\ {a}^(2) + 4 = 9 \\ {a}^(2) = 9 - 4 \\ {a}^(2) = 5 \\ a = √(5)`

2.

`{3}^(2) + {b}^(2) = {6}^(2) \\ 9 + {b}^(2) = 36 \\ {b}^(2) = 36 - 9 \\ {b}^(2) = 27 \\ b = √(9 * 3) \\ b = 3 √(3)`

3.

`{4}^(2) + {6}^(2) = {c}^(2) \\ 16 + 36 = {c}^(2) \\ {c}^(2) = 52 \\ c = √(13 * 4) \\ c = 2 √(13)`

Hope this helps. - M

Answer 2

using formula

`{c}^(2) = {a}^(2) + {b}^(2)`
1)

`{3}^(2) = {a}^(2) + {2}^(2) \\ a = \sqrt{ {3}^(2) - {2}^(2) } \\ a = √(5)`
2)

`{6}^(2) = {3}^(2) + {b}^(2) \\ b = \sqrt{ {6}^(2) - {3}^(2) } \\ b = √(27) \\ b = √(9) √(3) \\ b = 3 √(3)`
3)

`{c}^(2) = {4}^(2) + {6}^(2) \\ c = \sqrt{ {4}^(2) + {6}^(2) } \\ c = √(52) \\ c = √(4) √(13) \\ c = 2 √(13)`