Question

PLEASE HELP IM JUST TRYING TO GRADUATE

A hotel has a square lobby. Management wants to reserve a smaller square area in stone to serve as the base of a new seating area. The side length of the seating area will be four meters less than the side length of the lobby, as shown below.



After purchasing materials, the manager noticed that two times the area of the seating area was equal to 16 square meters less than the area of the entire lobby.

Write and solve a system of equations to determine the dimensions of the whole lobby and the smaller seating area cutout.

A.
The lobby is 8 meters by 8 meters, and the seating area is 4 meters by 4 meters.
B.
The lobby is 6 meters by 6 meters, and the seating area is 4 meters by 4 meters.
C.
The lobby is 10 meters by 10 meters, and the seating area is 6 meters by 6 meters.
D.
The lobby is 12 meters by 12 meters, and the seating area is 8 meters by 8 meters.

Answer 1

If the length of lobby is l and length of seating area is s

First equation is l =s+4 and second is 2s∧2= l∧2 - 16

If we replace l in second equation we get 2s∧2=(s+4)∧2 -16

l=12 and s=8

Correct answer is D

Good luck!!!