a rectangle is made up of seven congruent rectangles: 4 on top, 3 on bottom. Area= 756. Watz da perimeter?

Answer 1

That's quite a fun question :o)

Let's start with congruent rectangles. Have a look at this link http://en.wikipedia.org/wiki/Congruence_%28geometry%29 it will tell you that congruent rectangles are the same shape, but perhaps rotated.

So let's imagine a rectangle. It's sides are length x and y. Let's say the shorter edge is labelled 'y' and the longer edge is labelled 'x'.

We've got four of them in a row and right next to each other; their longer sides can go down the page and the shorter sides go across the page.

Next we rotate our rectangle 90 degrees. Place three of these rectangles hard up against the bottom edge of the first four.

Because the rectangle's edge lengths are very carefully constructed, our seven rectangles form one big rectangle. We'll call the edge lengths of the big rectangle a and b.

How long are the big rectangle's edges? Let's look at the one that goes across the page (we'll call it 'a'). It's equal to four of our smaller rectangle's shorter edges (that's 4y) or three of the smaller rectangle's longer edges (that's 3x). So:
a = 4y = 3x

Now let's look at the shorter edge of the larger rectangle (length 'b'). It's equal to x+y. (If in doubt, draw the picture and label all the edges; it will help heaps). So
b = x+y

Now we also know that the area of the big rectangle is 756. How do you calculate area? It's the length times the height (or 'a' times 'b'). So:
ab = 756

If we replace 'a' and 'b' with what we worked out above, we get
4y(x+y) = 756
3x(x+y) = 756

That's two equations, and two unknown values (x and y), so you should be able to solve this.

The perimeter of the larger rectangle is 2a+2b. So, once you've worked out what x and y are, you can then calculate the answer to your question.

I hope that helps.

Answer 2

The area of the large rectangle = 756. The area of each small rectangle is 756/7 or 108 since they're all congruent. I don't know if you got a picture or not but the only way you can construct a large rectangle out of 7 smaller ones is if the 4 on the top are laying on their short sides and the three bottom ones are laying on their long sides. If you look at the horizontal line where the top and bottom row meet, you'll see that the 4 short sides = 3 long sides.

Now you kind have to make some guesses and check them out. 27 x 4 = 108 (area = length x width) but 27 x 3 (long sides) = 81 and 4 x 4 (short sides) = 16, so that doesn't work.

Keep multiplying different combinations and eventually you'll find that 12 x 9 = 108. Now, 12 x 3 (long sides) = 36 and 9 x 4 (short sides) = 36. So it looks like the dimensions of each small rectangle is 9 x 12. Now we can tackle tackle the big rectangle.

The long side of the big rectangle is made up of 4 short sides or 3 long sides so it is 36. The short side of the big rectangle is made up of one long side and one short side or 12 + 9 = 21.

The perimeter = 36 +36 + 21 + 21 = 114.

Answer 3

user-friendly! For the fringe, you ought to feature up all 4 aspects. 2 lengths of four a million/2 yards, 2 widths of three yards: 4 a million/2 + 4 a million/2 + 3 + 3 = 15 For the area, use the formula for a rectangle, area = length x top: 4 a million/2 x 3 = thirteen a million/2

Answer 4

136