Answer:
B. 121 I'm sorry if its not correct
Answer:
![NK = 15](https://tex.z-dn.net/?f=NK%20%3D%2015)
![JL = 26](https://tex.z-dn.net/?f=JL%20%3D%2026)
![KL = 19.85](https://tex.z-dn.net/?f=KL%20%3D%2019.85)
![\angle JKM =49](https://tex.z-dn.net/?f=%5Cangle%20JKM%20%3D49)
![\angle JML =41](https://tex.z-dn.net/?f=%5Cangle%20JML%20%3D41)
![\angle MLK = 90](https://tex.z-dn.net/?f=%5Cangle%20MLK%20%3D%2090)
![\angle MNL =90](https://tex.z-dn.net/?f=%5Cangle%20MNL%20%3D90)
![\angle KJL =41](https://tex.z-dn.net/?f=%5Cangle%20KJL%20%3D41)
Step-by-step explanation:
Given
![MK = 30](https://tex.z-dn.net/?f=MK%20%3D%2030)
![NL = 13](https://tex.z-dn.net/?f=NL%20%3D%2013)
![\angle MKL = 41](https://tex.z-dn.net/?f=%5Cangle%20MKL%20%3D%2041)
Solving (a): NK
MK is a diagonal and NK is half of the diagonal. So:
![NK = \frac{1}{2} * MK](https://tex.z-dn.net/?f=NK%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20MK)
![NK = \frac{1}{2} * 30](https://tex.z-dn.net/?f=NK%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%2030)
![NK = 15](https://tex.z-dn.net/?f=NK%20%3D%2015)
Solving (b): JL
JL is a diagonal, and it is twice of NL.
![JL = 2 * NL](https://tex.z-dn.net/?f=JL%20%3D%202%20%2A%20NL)
![JL = 2 * 13](https://tex.z-dn.net/?f=JL%20%3D%202%20%2A%2013)
![JL = 26](https://tex.z-dn.net/?f=JL%20%3D%2026)
Solving (c): KL
To solve for KL, we consider triangle KNL where:
![\angle KNL = 90](https://tex.z-dn.net/?f=%5Cangle%20KNL%20%3D%2090)
and
![KL^2 = NL^2 + NK^2](https://tex.z-dn.net/?f=KL%5E2%20%3D%20NL%5E2%20%2B%20NK%5E2)
![KL^2 = 13^2 + 15^2](https://tex.z-dn.net/?f=KL%5E2%20%3D%2013%5E2%20%2B%2015%5E2)
![KL^2 = 394](https://tex.z-dn.net/?f=KL%5E2%20%3D%20394)
![KL = \sqrt{394](https://tex.z-dn.net/?f=KL%20%3D%20%5Csqrt%7B394)
![KL = 19.85](https://tex.z-dn.net/?f=KL%20%3D%2019.85)
Solving (d - h):
To do this, we consider triangle JKN
-- diagonals bisect one another at right angle
Alternate interior angles are equal. So:
![\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41](https://tex.z-dn.net/?f=%5Cangle%20MKL%20%3D%20%5Cangle%20KMJ%20%3D%20%5Cangle%20KJL%20%3D%20%5Cangle%20JLM%20%3D%2041)
Similarly:
![\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41](https://tex.z-dn.net/?f=%5Cangle%20MKJ%20%3D%20%5Cangle%20KML%20%3D%20%5Cangle%20MJL%20%3D%20%5Cangle%20JLK%20%3D%2090%20-%2041)
![\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49](https://tex.z-dn.net/?f=%5Cangle%20MKJ%20%3D%20%5Cangle%20KML%20%3D%20%5Cangle%20MJL%20%3D%20%5Cangle%20JLK%20%3D%2049)
So:
![\angle JKM =49](https://tex.z-dn.net/?f=%5Cangle%20JKM%20%3D49)
![\angle JML =41](https://tex.z-dn.net/?f=%5Cangle%20JML%20%3D41)
![\angle MLK = \angle MLJ + \angle JLK](https://tex.z-dn.net/?f=%5Cangle%20MLK%20%3D%20%5Cangle%20MLJ%20%2B%20%5Cangle%20JLK)
![\angle MLK = 49 + 41](https://tex.z-dn.net/?f=%5Cangle%20MLK%20%3D%2049%20%2B%2041)
![\angle MLK = 90](https://tex.z-dn.net/?f=%5Cangle%20MLK%20%3D%2090)
![\angle MNL =90](https://tex.z-dn.net/?f=%5Cangle%20MNL%20%3D90)
![\angle KJL =41](https://tex.z-dn.net/?f=%5Cangle%20KJL%20%3D41)
Answer:
V = 8/125 cubic units
Step-by-step explanation:
This prism is actually a cube of side length 2/5.
The volume of a cube of side length s is V = s^3.
Here, the volume of the cube (rectangular prism) is V = (2/5)^3, or
V = 8/125 cubic units
Answer:
14x. ....................