SOLUTION: The school park has a rectangular flower bed measuring 15 meters by 20 meters. The school administrators plan to double the area by providing a fence of uniform distance around the
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Question 1166938: The school park has a rectangular flower bed measuring 15 meters by 20 meters. The school administrators plan to double the area by providing a fence of uniform distance around the flower bed. Find the area and perimeter of the fence to the nearest hundredths. Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the area of the fence is currently 15 * 20 = 300 square feet.
to double the area, it needs to become 600 square feet.
each side would have to be equal to sqrt(600) = 24.49489743
round to two decimal places (nearest hundredth) to get 24.50 feet on each side.
the perimeter of the fence would be equal to 4 * 24.49489743 = 97.97958971.
round to two decimal places to get 97.98.
the formulas used are:
area = length * width for the rectangle.
area = side squared for the square.
perimeter = 2 * (length + width) for the rectangle).
perimeter = 4 * side for the square.
all rounding is done at the end of each calculation.
Tutor Theo misread the problem, so his solution is conceptually incorrect.
I came to guide you in right direction.
The area of the garden is 15*20 = 30 square meters;
so the area inside the fence is 2*300 = 600 square meters.
Thus this part is solved: it is easy part.
Now let start working on the second question.
Lex x be the uniform distance around the flower bed.
Then the dimensions of the fence are (15+2x) meters width and (20+2x) meters length.
The area inside the fence is then (15+2x)*(20+2x).
From here you have this equation to determine x
(15+2x)*(20+2x) = 2*15*20 = 600.
Reduce this equation to the standard quadratic equation form and solve using the quadratic formula.
4x^2 + 70x - 300 = 0.
It has no solution/solutions in integer or rational numbers, so other solution methods (guessing or factoring)
do not work.
When you find the value of x, you determine the perimeters as
(15+2x) + (20+2x) + (15+2x) + 20+2x).
