SOLUTION: A rectangle garden is 10ft longer than it is wide. Its area is 875 ft squared. What are its dimensions?

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Question 105103This question is from textbook Precalculus
: A rectangle garden is 10ft longer than it is wide. Its area is 875 ft squared. What are its dimensions? This question is from textbook Precalculus

Answer by kmcruz09(38) About Me  (Show Source):
You can put this solution on YOUR website!
First, let as assume.
Let x = the width of the plot
x + 10 = length of the plot
Then the area is x(x + 10)
Since it is stated in the problem that the area is 875 square feet, our final equation will be:
x+%28x+%2B+10%29+=+875
Solve it:
x+%28x+%2B+10%29+=+875
x%5E2+%2B+10x+=+875
x%5E2+%2B+10x+%2B+-875+=+0
Applying the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%2810%29+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-875%29%29%29%2F%282%2A1%29
x+=+%28-10+%2B-+sqrt%28+100-%28-3500%29%29%29%2F2
x+=+%28-10+%2B-+sqrt%283600%29%29%2F2
x+=+%28-10+%2B-+60%29%2F2
Now we can solve for the two roots
x+=+%28-10+%2B+60%29%2F2 or x+=+%28-10+-+60%29%2F2
x+=+%2850%29%2F2 or x+=+%28-70%29%2F2
x+=+25 or x+=+-35
But since we are looking for a real positive number, let us take x+=+25 as our answer. Therefore, the width is 25 ft and the length is 35 ft.
Thank you. ~kmcruz09~