Thread: another difficult problem~~proving~~so hard >.<

a rectangle ABCD is cut into eight squares as shown on the pix. find the perimeter of the rectangle ABCD if the perimeter of the smallest square is 24cm


btw the required pix is attached

thanks guys!!! u rok

Originally Posted by fring

a rectangle ABCD is cut into eight squares as shown on the pix. find the perimeter of the rectangle ABCD if the perimeter of the smallest square is 24cm


btw the required pix is attached

thanks guys!!! u rok

The diagram does not show eight smaller squares it shows eight rectangles.


However if we suppose this is just badly drawn and that they should be
squares, then the bottom right square is 3x3 of the smallest square. The
one above it is 4x4 of the smallest sqare, so the height of the rectangle
id 7 times the height of the smallest square.

Similarly the length of the rectangle is four times twice the length of a side
of the smallest square plus three times the side of the smallest square.

Hence your rectangle has a height of seven times the side of the smallest
square, and a length of eleven times the side of the smallest square.

Therefore the perimiter of the rectangle is 2x7+2x11 times the side of the
smallest square. Since you are told the perimiter of the smallest square you
can find its side, and so the final answer.

RonL

Hello, fring!

A rectangle ABCD is cut into eight squares as shown on the pix.
Find the perimeter of the rectangle ABCD
if the perimeter of the smallest square is 24cm

Code:

                                 (1) 
                    a             ↓       b
      o - - - - - - - - - - - - - o - - - - - - - o
      |                           |               |
      |                           |               |
      |                           |               |
      |                           |b              |b
     a|                           |               |
      |                           |               |
      |                           | 6       c     |
      |                           o - o - - - - - o ← (2)
      |                          6|   |6          |
(4) → o - - - o - - - o - - - o - o - o           |
      |       |       |       |       |           | c
     d|       |       |       |       |d          |
      |       |       |       |       |           |
      o - - - o - - - o - - - o - - - o - - - - - o
          d       d       d       d   ↑     c
                                     (3)

At (1) we see that: .

At (2) we see that: .

At (3) we see that: .

. . Hence: . [1]


At (4) we see that: . [2]


Equate [1] and [2]: .

Now you can determine and the perimeter of the rectangle.

Let,
length of each side of the smallest square = a
" " " " " " 3rd largest square = b
Then, we have
length of each side of the 2nd largest square = a+b
" " " " " " 2nd smallest " = b-a
" " " " " " largest " = 4b-5a
Now, since ABCD is a rectangle,
therefore, AD=BC
=>(4b-5a)+(b-a) = (a+b)+b
=>b = 7a/3------------------I
Given,
perimeter of the smallest square = 24cm.
=>4a = 24cm.
=>a = 6cm.
Putting the value of a in eq.I, we have
b = 14cm.
Now, we can calculate the perimeter of ABCD.
It comes out to be 160cm.