SOLUTION: I seem to be really stuck on this question.
A rectangular picture is to be surrounded by a frame. The dimension of the frame is 24 inches by 32 inches. Let w be the width of the
Algebra.Com
Question 795585: I seem to be really stuck on this question.
A rectangular picture is to be surrounded by a frame. The dimension of the frame is 24 inches by 32 inches. Let w be the width of the frame.
Write an equation for the area of the picture in terms of the width of the frame
A(w)=
I've tried 4(w+24)4(w+32), 2(w+24) 2(w+36), (4w+24) (4w+36) and (2w+24)(2w+36)
The second part to the question is: If the area of the picture itself is 560 square inches, determine the width of the frame. It wants the width in inches.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular picture is to be surrounded by a frame.
The dimension of the frame is 24 inches by 32 inches.
Let w be the width of the frame.
Write an equation for the area of the picture in terms of the width of the frame
:
A frame with a width w, subtracts 2w from the overall dimension to get the picture dimensions, therefore
A(w)= (24-2w)(32-2w)
FOIL
A(w) = 768 - 48w - 64w + 4w^2
A quadratic equation
A(w) = 4w^2 - 112w + 768
:
If the area of the picture itself is 560 square inches, determine the width of the frame.
A(w) = 560, therefore:
4w^2 - 112w + 768 = 560
4w^2 - 112w + 768 - 50 = 0
4w^2 - 112w + 208 = 0
simplify, divide by 4
w^2 - 28w + 52 = 0
Factors to
(w-26)(w-2) = 0
Two solutions
w = 26 in, not possible, throw this solution out
and
w = 2 inches is the width of the frame, makes sense
:
:
Check it by finding the area of the picture with w=2
(24-4)*(32-4) = 560, area of the picture
RELATED QUESTIONS
a rectangular picture with dimension 20 cm by 15 cm is to be framed. What are the... (answered by 303795)
A rectangular picture is 3 cm longer than it is wide. The picture is surrounded by a... (answered by ankor@dixie-net.com)
A rectangular picture frame measures 20cm by 30cm. A new frame is to made by increasing... (answered by unlockmath)
A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with uniform... (answered by checkley77)
A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with uniform... (answered by Jk22)
A rectangular picture measuring 4 in. by 10 in. is surrounded by a frame with uniform... (answered by Stitch)
A rectangular photo of dimensions 7 cm by 8 cm is placed in a picture frame of uniform... (answered by josgarithmetic)
A square picture is surrounded by a rectangular frame. The length of the framae's... (answered by josgarithmetic)
A 5 by seven inch rectangular picture has a frame of uniform width.If the outer edge of... (answered by mananth)