Dimensions- Picture

[Guest]

A rectangular picture is placed in a frame 2 inches wide.

Frame area- 152 square inches.

Length of frame is twice the width.

Calculate the dimensions of the picture.

[burgess]

A rectangular picture is placed in a frame 2 inches wide.

Frame area- 152 square inches.

Length of frame is twice the width.

Calculate the dimensions of the picture.

L=2B

Area = length *breadth= 2B * B=152

You will get length and breadth, and from the answer reduce 2 inch you will get picture dimensions

[Guest]

2B * B = 152

2B^2 = 152

How do I proceed from here ?

Thanks.

[Guest]

W = width of frame
2W = length of frame

First get expression for area of frame.....

(2W x 4) + 4(W - 4) = 152

8W + 4W - 16 = 152

12W = 168

W = 14 = Width of frame
Length of frame = 28

Dimensions of picture
Width = 10 inches
Length = 24 inches

[Guest]

"(2W x 4) + 4(W - 4) = 152"

I am not clear on the equation.

Also, one question:

Is the 4 inch difference in dimensions between the frame and picture due to the 2 inch frame and 4 sides?

[Guest]

We were told in the question that the area of the frame is 152 square inches.
And the Length of the frame is twice its width. So L = 2W.
I assume the frame is around the picture and the picture is placed in the middle of it to leave a border of 2 inches.
We are told the frame is 2 inches wide so I assume that means the border around the picture is 2 inches wide.
I assume the Length of the frame means the length of the outside edge of the longest side of frame with the picture in it. Not the length around the perimeter of the frame, and the width of the frame is the length of the outer edge of the short side of the frame with the picture in it.

I then try to set up an expression in terms of the width W, length 2W and "frame width" 2 inches.
This is equal to 152 sq. inches.

First imagine the frame with picture inside and frame cut in 4 pieces....... draw a line along the top and bottom of the picture along the length.
This gives the frame top piece 2W long by 2 inches wide and there is the bottom frame piece the same size.
So that gives (2W x 2) x 2 ..... or....(2W x 4) sq. inches

Then there are the 2 short pieces of frame at either side.......
This has length (W - 4) ... and width 2 inches .... and there are 2 of them as well
So that gives (W - 4) x 2 x2 .... gives... 4(W - 4) sq. inches

Now if we add these bits together it will give the area of the frame border which we are told is 152.
(2W x 4) + 4(W - 4) = 152

then work out the brackets, simplify and solve the equation........

8W + 4W - 16 = 152

12W = 168

W = 14 = Width of frame
Length of frame = 28 .....from L = 2W

Dimensions of the picture.....picture is inside the frame so take 2 inches off each side.....take 4 inches off....

Picture Width = 10 inches
Picture Length = 24 inches

Surely this must be self explanatory..........

[Guest]

I understand it now. Thanks.