You are here:

# Advanced Math/Frame and Picture Dimensions # 2

Question
If a picture is placed in a frame 2 inches wide and frame area is 87 square inches, what are picture dimensions?

Let:
L- Length

W- Width

Dimensions of frame:

Length- 10.25 inches *
Width- 8.5 inches *

* 8 x 10 frame.

Frame- 2 inches wide

Frame area- 87 in.^2

Picture dimensions:

Length- 6.5 inches *

Width- 4.5 inches *

* 4 x 6 picture

I was attempting to use the formula to calculate with actually measuring frame and picture.

Which measurement to use for length is X larger than width for frame?

10.25/8.5 = 1.20

8/5/10.25 = .829

10.25-8.5 = 1.75

My solution (not sure):

L X W = LW Total Area of frame and picture.

(L-4)(W-4)= LW - 4W - 4L + 16 in.^2

LW - (LW - 4W - 4L + 16) = 87

4W + 4L = 103

W + L = 25.75

How do I proceed from here?

Thanks.

"If a picture is placed in a frame 2 inches wide and frame area is 87 square inches, what are picture dimensions?"
You can't tell, because there are an infinite number of solutions.

Let L and W be the length and width of the picture.
The frame will have a 4" square in each corner, contributing 16 inē of area.

remaining area of frame = 2(2L) + 2(2W) = 4(L+W)
4(L+W) = 87 - 16 = 71 inē
L+W = 71/4 = 17.75 in
W = 17.75 - L
The picture can have any positive length less than 17.75".

For example, if the picture is 10" long then its width is 7.75" and area = 77.5 inē.
area of picture + frame = (10+4)(7.75+4) = 164.5 inē
area of frame = 164.5 - 77.5 = 87 inē

If the picture is 9" long then its width is 8.75 and area = 78.75 inē.
area of picture + frame = (9+4)(8.75+4) = 165.75 inē
area of frame = 165.75 - 78.75 = 87 inē
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Fast, courteous, and clear solution !!

Volunteer

#### Janet Yang

##### Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

##### Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.