Question

The length of a rectangular room is 5 feet longer than twice the width If the room's perimeter is 166 feet, what is the length?
A. 67 feet
B. 44 feet
C. None of these
D. 114 feet
E. 57 feet

Answer 1

Answer:

E. 57 feet

Step-by-step explanation:

If you draw a rectangle and label the long side 5+2x, and the short side x, then that represents the rectangular floor.

The 2x is "twice the width".

The 5 added to the 2x is "5 feet longer than"

The x is the width of the room.

                                                                                   

If the equation for the whole perimeter is 2(5+2x)+2x=166 <-(The perimeter)

                                     (Both of the long sides)^       ^(Both of the short sides)

Then we need to solve for x.

$2(5+2x)+2x=166\\10+4x+2x=166\\10+6x=166\\6x=156\\x=26$

Next, we input the value we got into the equation 5+2x (The length of one side) and solve

$5+2x\\5+2(26)\\5+52\\57$

So the length of the room is 57 feet.

Hope this helps!