solve this as soon as you can or possible...

Question

Rectangle A has a length of 80 inches and a width of 30 inches. Rectangle A has the same area as Rectangle B, but has different dimensions. The width of Rectangle B is 80% shorter than the width of Rectangle A as shown.    

 

Which percent represents how much longer the length of Rectangle B must be to maintain the same area as Rectangle A?

 

 

  It must be 30% longer than Rectangle A.

  It must be 60% longer than Rectangle A.

  It must be 80% longer than Rectangle A.

  It must be 400% longer than Rectangle A.

Answer 1

This problem is a great example of T.M.I. (too much information).  Since the relationship of Rectangle B to Rectangle A is given as a percent and the problem requests that we answer in percent, then we don't need to know the actual dimensions or even to see the picture!

 

Area = length * width

 

Number the rectangles 'a' and 'b', and set their areas equal:

        Area  = L_a * W_b  = La * W_b

 

Now, confusion:  The phrase, "width of Rectangle B is 80% shorter than the width of Rectangle A" is often not understood,  Does it mean  W_b = 0.80*W_a  (they should have said, "the width of Rectangle B is 80% as long as Rectangle A") or does it mean  W_b = W_a - 0.80*W_a ?  Let's take the second meaning --  So, W_b = 0.20*W_a

 

   Area  = L_a * W_b  = L_a * W_b

               L_a * W_a  = L_b * 0.20*W_a                   (replace W_b)

               W_a / (0.20*W_a) = L_b / L_b                (find ratio which gives us percent when we multiply by 100%)

               5 = L_b / L_a   =  500%

 

(Similar wording dilemma)    The width of Rectangle B is 5 times the width of Rectangle A, but

     Rectangle B is 400% longer than Rectangle A.

Answer 2

Rectangle A has an area of 80(30) = 2400 in².

 

 

 

The width of Rectangle B is 80% shorter than the width of Rectangle A. This means it is the width of A minus 80% of A:

 

30 - 0.8(30) = 6 inches

 

 

 

Let's call x the length of Rectangle B. Then:

 

6x = 2400

x = 400

 

 

 

What is the relationship between the 80-inch length of Rectangle A and the 400-inch length of Rectangle B?

 

80 + 80y = 400

80y = 320

y = 4

 

This means that Rectangle B is 400% longer (5 times longer) than Rectangle A.

 

 

 

Another way to solve this:

 

In order to make the width 80% shorter, you multiply it by 0.2 (so it becomes 20% as long). So, how can we undo that in the rectangle's length? Divide the length by 0.2. That's the same as multiplying it by 1/0.2 = 5.

 

So, Rectangle B is 5 times as long as, or 400% longer than, Rectangle A.