Question 483452: A rectangular table can be be set against one wall of a room, as shown, so that it is 5 feet from the two side walls and 8 feet from the fourth wall. If the perimeter of the room is 58 feet and the combined length of the three exposed sides of the table is 17.5 feet, then what are the dimensions of the table?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular table can be be set against one wall of a room, as shown, so that it is 5 feet from the two side walls and 8 feet from the fourth wall.
If the perimeter of the room is 58 feet
:
let x = length of the table against the wall
let y = the width of the table
the room perimeter equation
2(x+10) + 2(y+8) = 58
2x + 20 + 2y + 16 = 58
2x + 2y + 36 = 58
2x + 2y = 58 - 36
2x + 2y = 22
simplify, divide by 2
x + y = 11
:
"and the combined length of the three exposed sides of the table is 17.5 feet,"
x + 2y = 17.5
:
Use elimination with these two equations
x + 2y = 17.5
x + 2 = 11
---------------subtraction eliminates x, find y
y = 6.5 ft is the width of the table
:
Find x:
x + y = 11
x + 6.5 = 11
x = 11 - 6.5
x = 4.5 ft is the length of the table against the wall
:
then what are the dimensions of the table? 6.5' by 4.5'
;
:
Check solution in the room perimeter equation
2(4.5+10) + 2(6.5+8) =
|
|
|
