SOLUTION: a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared.
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Question 166509: a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared.
:
Let x = width of the picture
then
(x+1) = length of the picture
:
Frame 1/2 inch wider all around, therefore
x + 2(.5)=
(x+1) = width of the frame
and
(x+1) + 2(.5) =
x + 1 + 1 =
(x+2) = length of the the frame
:
Frame area given as 8 sq/in, therefore
(x+1)*(x+2) = 8
FOIL
x^2 + 3x + 2 = 8
x^2 + 3x + 2 - 8 = 0
:
a quadratic equation
x^2 + 3x - 6 = 0
Use the quadratic formula to find x: a=1; b=3; c=-6
:
You should get a positive solution about x = 1.37 inches is the width of the pic
then, 2.37 = length
:
A = 1.37 * 2.37
A = 3.25 sq/in is the picture
:
:
Check solution: Frame dimensions 2.37 by 3.37
Frame area = 2.37 * 3.37 = 7.77 ~ 8 sq/in as given
