SOLUTION: A 12 inch by 18 inch rectangular picture is to have a frame of uniform width. If the perimeter of the framed picture is 84 inches, determine the width of the frame.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A 12 inch by 18 inch rectangular picture is to have a frame of uniform width. If the perimeter of the framed picture is 84 inches, determine the width of the frame.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 56948This question is from textbook Introductory Algebra for College Students
: A 12 inch by 18 inch rectangular picture is to have a frame of uniform width. If the perimeter of the framed picture is 84 inches, determine the width of the frame. This question is from textbook Introductory Algebra for College Students

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A 12 inch by 18 inch rectangular picture is to have a frame of uniform width. If the perimeter of the framed picture is 84 inches, determine the width of the frame.
:
Draw a rough diagram, it will make it easy to understand. Label the picture 12 by 18. Label the width of the frame to the picture as x. Then the you can label the frame as (12+2x) by (18+2x)"
:
They give the perimeter of the frame:
2W + 2L = 84; we have W = (12+2x); L = (12+2x)
Which is:
2(12+2x) + 2(18+2x) = 84
24 + 4x + 36 + 4x = 84
8x + 60 = 84
8x = 84 - 60
8x = 24
x = 24/8
x = 3 inches is the width of the uniform width around the picture
:
The frame dimensions: (12+6) by (18+6) is 18 by 24
:
Check using the perimeter:
2(18) + 2(24) =
36 + 48 = 84