Question 1200737
.
Five centimeters are cut off (along one side of) of a square sheet of paper and 8 cm 
are added to the adjacent side. The resulting rectangular sheet of paper has a perimeter of 98 cm.
a) What was the area of the original square piece of paper?
b) What is the length of the diagonal of the resulting rectangular piece of paper?
~~~~~~~~~~~~~~~~~~~~


<pre>
It was originally: a square x cm by x cm.

It is now: a rectangle (x-5) cm by (x+8) cm.


To find x, use an equation for the perimeter of the rectangle

    2(x-5) + 2(x+8) = 98  cm.


Simplify and find x

    2x - 10 + 2x + 16 = 98

         4x           = 98 + 10 - 16

         4x           =    92

          x           = 92/4 = 23.


The area of the original peace of paper was x^2 = 23^2 = 529 cm^2.    <U>ANSWER</U> to (a)


The diagonal of the resulting rectangle is

    d = {{{sqrt((23-5)^2 + (23+8)^2)}}} = {{{sqrt(1285)}}} = 35.8469 cm  (approximately).   <U>ANSWER</U> to (b)
</pre>

Solved.