Ana' location is further away from the entrance
Answer:
The lengths of the bases are 9 inches and 15 inches.
Step-by-step explanation:
The area of trapezoid is
![=\frac12(\textrm{ sum of parallel sides})\times height](https://tex.z-dn.net/?f=%3D%5Cfrac12%28%5Ctextrm%7B%20sum%20of%20parallel%20sides%7D%29%5Ctimes%20height)
Given that the height of a trapezoid is 8 in. and its area is 96 in².
Assume the bases of the trapezoid be b₁ and b₂.
Since one base of the trapezoid 6 in. longer than the other.
Let, b₁=b₂+6
The area of the trapezoid is
in²
in²
in²
According to the problem,
![\frac12(2b_2+6)\times8 =96](https://tex.z-dn.net/?f=%5Cfrac12%282b_2%2B6%29%5Ctimes8%20%3D96)
[ Multiplying
]
![\Rightarrow 2b_2+6=24](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%2B6%3D24)
![\Rightarrow 2b_2=24-6](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%3D24-6)
![\Rightarrow 2b_2=18](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%3D18)
![\Rightarrow b_2=\frac{18}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20b_2%3D%5Cfrac%7B18%7D%7B2%7D)
![\Rightarrow b_2=9](https://tex.z-dn.net/?f=%5CRightarrow%20b_2%3D9)
Then, ![b_1=b_2+6](https://tex.z-dn.net/?f=b_1%3Db_2%2B6)
=9+6
=15 in
The lengths of the bases are 9 inches and 15 inches.
I’m pretty sure it’s A sorry if I’m wrong