SOLUTION: DIMENSIONS OF A GARDEN: A rectangular garden is 10ft. longer than it is wide. Its area is 875ft.^2. What are its dImensions?

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Question 199319This question is from textbook algebra and trigonometry
: DIMENSIONS OF A GARDEN: A rectangular garden is 10ft. longer than it is wide. Its area is 875ft.^2. What are its dImensions? This question is from textbook algebra and trigonometry

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given:
Area = 875 sq ft
Length = Width + 10ft
Width = W

We know Area of a Rectangle = L x W
So,
875ft%5E2+=+%28W%2B10%29%28W%29
875=W%5E2%2B10W
W%5E2%2B10W-875=0, wheresystem%28a=1%2Cb=10%2Cc=-875%29

By Quadratic,
W=x
Solving discriminant: b%5E2-4ac=10%5E2-4%281%29%28-875%29=100%2B3500=3600
So,
x=%28-10%2B-sqrt%283600%29%29%2F%282%2A1%29=%28-10%2B-60%29%2F2
x=%28-10%2B60%29%2F2=50%2F2=red%2825ft%29, Width
x=%28-10-60%29%2F2=-70%2F2=-35, disregard "-"


Having Width = 25ft,
Length = 10ft + 25ft = 35ft

Check on the Area:
875ft%5E2=35%2A25
875ft%5E2=875ft%5E2

Thank you,
Jojo