SOLUTION: Wendy wants to build a frame of uniform width around the outside of her 21cm x 30cm photo but she can only afford 188cm² of wood for the frame. How wide will the frame be?

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Question 1207376: Wendy wants to build a frame of uniform width around the outside of her 21cm x 30cm photo but she can only afford 188cm² of wood for the frame. How wide will the frame be?
Found 4 solutions by josgarithmetic, Edwin McCravy, mccravyedwin, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
You should draw the description and label the parts to help see.
w, the frame's uniform width; everything is rectangular shaped.

Whole area including the frame


Just the area of the frame
------------Simplify and solve this for w.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!




The frame is four rectangles, two are (30+x) by x and two are (21+x) by x.

So



That simplifies to: 



Divide through by 2:



Solve by the quadratic formula:

 

 

 

Ignore the minus



About x = 1.726273692 cm = width of frame.  Round off as you were told. 

Edwin
Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!




The frame is the large rectangle minus the small rectangle.

Let x be the width of the frame, so the large rectangle is 

30+2x by 21+2x  and the small rectangle is 30 by 21 or 630.

So their difference must equal 188



That simplifies to: 



Divide through by 2:



Solve by the quadratic formula:

 

 

 

Ignore the minus



About x = 1.726273692 cm = width of frame.  Round off as you were told. 

Edwin
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

If you want to see many other similar solved problems,  look into the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Cynthia Besch wants to buy a rug for a room
    - Problems on a circular pool and a walkway around it
in this site.   Learn the subject from there.



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