CAN SOMEONE PLEASE HELP ME WITH THIS SHORT MATH PROBLEM? (i really need help)?

Question

i have an semester exam tomorrow and i still don't understand this so i really need help :(

the image is here: http://i11.tinypic.com/47ck386.jpg

"FIND THE MISSING AREAS AND DIMENSIONS FOR EACH GENERIC RECTANGLE BELOW. THEN WRITE EACH AREA AS A SUM AND AS A PRODUCT"

please help!!!!

Answer 1

So that it will be easy for you to understand how to solve this, FIRST, let us make a standard reference to your drawing. Based on your drawing, we will go counterclockwise with the 16x^2 as indicated as Rectangle/Square 1 or R1, upper right rectangle as R2, bottom right is R3 and bottom left is R4.

You have the upper left corner R1 with an area of 16x^2 and this is true because the given dimension of one side as 8x.To get an area of 16x^2 then the other side must be 8x because 8x multiplied by 8x, gives you the area (8x)(8x) or 16x^2. Now on the bottom right corner R3 is an area equal to 1. This means the dimensions are 1 and 1.

Now to figure out the upper RIGHT rectangle R2 means that the top boundary line is 1 and the right vertical boundary line is 8x. The area is then, (8x)(1) or just 8x.

The rectangle R4 has a left vertical boundary line equal to 1 and the bottom boundary line as 8x. Just like R2 the area is 8x.

The dimensions of the whole big rectangle containing all R1, R2, R3 and R4 are 8x+1 and 8x+1

Answer 2

All the areas are 16x^2 or 8x X 8x

if 16x^2 =1
then x = (1/16)^1/2

Answer 3

Pay no attention to Yahya. He thinks that 8x * 8x is 16x^2, but it's 64x^2.

You, and he, might like to know that 8x * 2x is 16x^2.

Those are rectangles, right, not squares?

Answer 4

is the 8x on the left side the height of the entire rectangle or the height of the little rectangle that it is next to?

Answer 5

The upper left rectangle has dimensions.

8xy = 16x²
y = 16x²/(8x) = 2x

Upper left rectangle is 8x*2x = 16x²
_______________

Lower right rectangle has dimensions

uv = 1
u = 1/v

Lower right rectangle is v(1/v) = 1
_________________

Upper right rectangle is 8x(1/v) = 8x/v

Lower left rectangle is 2x*v = 2xv

Large rectangle is (8x + v)(2x + 1/v) = 16x² + 8x/v + 2xv + 1