Asked by kim
The dimensions of a playground are 50 feet by 75 feet. You want
to double its area by adding the same distance x to the length and
width. Find x and the new dimensions of the playground.
to double its area by adding the same distance x to the length and
width. Find x and the new dimensions of the playground.
Answers
Answered by
Reiny
distance to be added = x
original area = 50x75 = 3750 ft^2
double that area = 7500 ft^2
(50+x)(75+x) = 7500
3750 + 125x + x^2 = 7500
x^2 + 125x - 3750 = 0
(x+150)(x-25) = 0
x = 25 or x is a negative
25 feet should be added to each dimension
check:
new length = 100
new width = 75
new area = 7500 , which is twice the original,
all is good
original area = 50x75 = 3750 ft^2
double that area = 7500 ft^2
(50+x)(75+x) = 7500
3750 + 125x + x^2 = 7500
x^2 + 125x - 3750 = 0
(x+150)(x-25) = 0
x = 25 or x is a negative
25 feet should be added to each dimension
check:
new length = 100
new width = 75
new area = 7500 , which is twice the original,
all is good
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