Question

Use the Pythagorean Theorem to find the missing lengths

Answer 1

4) c = 10

5) b = 10

6) b = 12

7) a = 4

Explanation:

Pythagorean Theorem = a^2 + b^2 = c^2

to solve these, just substitute a, b, and c for the values given.

4) a = 8, b = 6

a^2 + b^2 = c^2

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c =
`√(100)`

c = 10

5) a = 24, c = 26

a^2 + b^2 = c^2

24^2 + b^2 = 26^2

576 + b^2 = 676

subtract 576 from both sides

b^2 = 676 - 576

b^2 = 100

b = 10

6) a = 5, c = 13

a^2 + b^2 = c^2

5^2 + b^2 = 13^2

25 + b^2 = 169

subtract 25 from both sides

b^2 = 169 - 25

b^2 = 144

b = 12

7) b = 11, c =
`√(137)`

a^2 + b^2 = c^2

a^2 + 11^2 = 137

a^2 + 121 = 137

a^2 = 137 - 121

a^2 = 16

a = 4