SOLUTION: A framed painting has overall dimensions of 32"x29". the area of the painting itself is 550sq". Find the width of the fame. Please show the work. Thank you!

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Question 1074358: A framed painting has overall dimensions of 32"x29". the area of the painting itself is 550sq". Find the width of the fame. Please show the work. Thank you!
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
A key to this question is that they are assuming the
width of the frame is uniform all around
Let the width of the frame =
------------------------------------------------
I will subtract the width of the frame from BOTH sides
of the overall width AND the overall height to get the
dimensions of the painting itself
--------------------------------------------------




Use the quadratic formula







( the positive square root is too big )


The width of the frame is 3.5 inches
---------------------------------
check:





OK

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Assuming the width of the frame uniform, let x be the frame width.


Then the dimensions of the painting itself are 32-2x and 29-2x inches.

The area equation for the painting is

(32-2x)*(29-2x) = 550.

Simplify and solve for x.


For many other similar solved problems see the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".



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