SOLUTION: 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

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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?

Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
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let the sides of the squar be equal to x.
if you take 5 cm off one side, then that side is equal to x - 5.
if you add 8 cm to the other side, then that side is equal to x + 8.
the resulting rectangle has two sides that are x - 5 and two sides that are x + 8.
the resulting permieter is equal to 2 * (x - 5) + 2 * (x + 8).
simplify to get 2x - 10 + 2x + 16
combine like terms to get 4x + 6
that is the perimeter.
since the perimeter is equal to 98, you get 4x + 6 = 98
subtract 6 from voth sides of the equation to get 4x = 92
solve for x to get x = 92/4 = 23.
the area of the original square is x^2 = 23^2 = 529 square cm.
the resulting rectangle is 23 - 5 by 23 + 8 = 18 by 31.
the diagonals form a right triangle with a height of 31 and a base of 18.
the diagonal is the hypotenuse of this right triangle.
the length of the diagonal is equal to sqrt(18^2 + 31^2) = sqrt(1285).
this is equal to 35.84689666

Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
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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.    ANSWER to (a)


The diagonal of the resulting rectangle is

    d = sqrt%28%2823-5%29%5E2+%2B+%2823%2B8%29%5E2%29 = sqrt%281285%29 = 35.8469 cm  (approximately).   ANSWER to (b)

Solved.