Help please! A rectangular room is 1.9 times as long as it is wide, and its perimeter is 32 meters. Find the dimension of the room.

Question

whpalmer4 · Answer

This a straightforward word  problem to convert into an equation.  You know the area of a rectangle = length * width, right?  And perimeter is the sum of all of the sides, so length + length + width + width = 2*length + 2*width.  We are told that length = width * 1.9, and perimeter = 32.  Write it all as equations:

$$L = W*1.9$$$$32 = 2*L + 2*W$$

Now solve for L and W by substitution or elimination.  As you've already got an expression for L in terms of W that requires no manipulation, I would suggest substituting that into the other equation, which will give you an equation only in terms of W.  Solve that, then plug your answer back into the first equation to find L.

anonymous · Answer

But I still dont know what the W is.

whpalmer4 · Answer

You could also write it in terms of the width directly:

32 = 2*(W*1.9) + 2*W

and solve that for W, and multiply the result by 1.9 to get L.

whpalmer4 · Answer

W is the width of the room, L is the length.  Or are you saying you don't see how to find W?

anonymous · Answer

Oh wait so I do 2(1.9) then subtract that answer from 32 and I get the width?

whpalmer4 · Answer

Let's back up.  Do you understand the formulas for area and perimeter?

anonymous · Answer

Yes. I got the answer. I figured out how to work it. Thank you.