Question 314212: Hi,
I cant even get started on this problem after reviewing my textbook all day. Any help is greatly appreciated!
14 Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A rectangular cabinet door has a 20 inch by 38 inch glass panel in the center with a uniform wooden edge around the glass. If the area of the wooden edge is 248 square inches, how wide is the wooden edge?
Thank you, Daniel
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Solve using the five-step problem-solving process.
Show all steps necessary to arrive at your solution.
A rectangular cabinet door has a 20 inch by 38 inch glass panel in the center
with a uniform wooden edge around the glass.
If the area of the wooden edge is 248 square inches, how wide is the wooden edge?
:
Let x = the width of the wooden edge
:
Find the total area of the glass and the edge
(20*38) + 248 = 1008 sq/in
:
The dimensions of the total area, which include the wooden edge, will be:
(2x+20) by (2x+38)
:
The total area equation
(2x+20) * (2x+38) = 1008
FOIL
4x^2 + 76x + 40x + 760 = 1008
Arrange as a quadratic equation
4x^2 + 116x + 760 - 1008 = 0
:
4x^2 + 116x - 248 = 0
Simplify, divide by 4, resulting in
x^2 + 29x - 62 = 0
Factors to
(x+31)(x-2) = 0
positive solution only is what we want here
x = 2 in is the width of the wooden edge
:
:
Check solution finding the difference in area
24 * 42 = 1008, overall area
20 * 38 = 760, glass area
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differ: = 348, given area of wooden edge
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