Select the correct answer from each drop-down menu.

Mathematics

1 answer:

ankoles [38]3 years ago

3 0

Answer:

AB = 14
AC = 19.8 ≈ 20

Step-by-step explanation:

The Pythagorean theorem can be used to find the lengths of the segments at the top of the square. The left one is found from ...

FA² = FE² +EA²

13² -12² = EA² = 169 -144 = 25

EA = √25 = 5

The right one is found from ...

FB² = FE² +EB²

15² -12² = EB² = 225 -144 = 81

EB = √81 = 9

Then the length of the side of the square is ...

AB = AE +EB = 5 +9

AB = 14

The length of the diagonal can also be found using the Pythagorean theorem.

AC² = AB² +BC² = 14² +14²

AC = √(196 +196) = 14√2 ≈ 19.7990

Rounded to the nearest integer, AC ≈ 20.

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