SOLUTION: Sirs/Madams, Kindly help my son in solving one item in his assignment. He was able to solve the other items except for this one. We will greatly appreciate your help. "The Le

Question 257447: Sirs/Madams,
Kindly help my son in solving one item in his assignment. He was able to solve the other items except for this one. We will greatly appreciate your help.
"The Length of a picture is four/thirds (4/3) times its Width. It is placed in a picture frame of uniform width of 2 centimeters. If the area of the frame is 100 square centimeters, what are the dimensions of the picture?"
Thank you very much for your help.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Let x = the width of the picture.
Then, since the length is 4/3 of the width, the length of the picture is

Let's look at a picture of the situation:

The inner rectangle is the picture.

The four outer rectangles make up the frame. The two larger rectangles, top and bottom, have a length of 2 + x + 2 or x+4 and a width of 2. The area of each is (x+4)2 = 2x+8.

The two smaller rectangles on the sides have a length of 4x/3 and a width of 2. The area of each is 4x/3*2 = 8x/3.

The combined areas of the four rectangles is 2x+8 + 2x+8 + 8x/3 + 8x/3 = 4x+16+16x/3. We are told that the area of the frame is 100 square centimeters. So

We can use Algebra to solve this. We'll start by eliminating the fraction by multiplying both sides by 3:

which simplifies to:

Subtracting 48 from each side we get:

Dividing both sides by 28 we get:

Since x is the width of the picture the width is 9 centimeters. The length picture is 4x/3 = 4(9)/3 = 12 centimeters.
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