Question

Is this correct if not why quickkkkkk!!!!!

Answer 1

14.42

Explanation:

First, find the length of the leg of the bigger triangle (not the overall big triangle) using the Pythagorean Theorem. The overall length is 24, but we don't know the leg of the bigger triangle or the little triangle, so that is why we are going to find the length of the bigger triangle's leg. b = 12 and c = 20.

`a^(2) + b^(2) =c^(2) \\a^(2) +12^(2) =20^(2) \\a^(2) +144=400\\a^(2) +144-144=400-144\\a^(2) =256\\\sqrt{a^(2)} =√(256)\\a = 16`

Next, find the leg of the little triangle by subtraction

24 - 16 = 8

Finally, you can find the hypotenuse of the little triangle by using the Pythagorean Theorem. a = 12 and b = 8

`a^(2) + b^(2) =c^(2) \\12^(2) +8^(2) =2c^(2) \\64 +144=c^(2)\\208 = c^(2) \\√(208)=\sqrt{c^(2)} \\ c = 14.42`