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

using formula
${c}^{2} = {a}^{2} + {b}^{2}$
1)
${3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5}$
2)
${6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3}$
3)
${c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13}$

Answer 2

Hey there!

Solve them by using
${a}^{2} + {b}^{2} = {c}^{2}$


1.
${a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5}$

2.
${3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3}$

3.
${4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13}$

Hope this helps. - M