Answer:
[tex]\sqrt{41}[/tex] = x
Step-by-step explanation:
Basically, find the missing side lengths of each triangle so that you can solve for x:
1. right triangle w/ side lengths 48 and 52
- 48^2 + (missing side)^2 = 52^2
- 2304 + (missing side)^2 = 2704
- (missing side)^2 = 400
- (missing side) = 20 (use this for next triangle)
2. right triangle w/ side lengths 12 and 20 (from previous triangle)
- 12^2 + (missing side)^2 = 20^2
- 144 + (missing side)^2 = 400
- (missing side)^2 = 256
- (missing side) = 16 (will be used with next triangle's missing side)
3. right triangle w/ side lengths 5 and 13
- 5^2 + (missing side)^2 = 13^2
- 25 + (missing side)^2 = 169
- (missing side)^2 =144
- (missing side) = 12
Take right triangle w/ side lengths 12, 20, and 16 (#2) and right triangle w/ side lengths 5, 13, and 12 (#3):
- the value of 12 (missing side of #3) subtracted from the #2's missing side, 16, (not its hypotenuse that equals 20 which was found from #1) will equal the missing side length that will be used to find 'x'
- 16 - 12 = 4 ---> so the side lengths are 4, 5, and x
4. Solve for the final triangle that includes x:
- 4^2 + 5^2 = x^2
- 16 + 25 = x^2
- 41 = x^2
- [tex]\sqrt{41}[/tex] = x
