SOLUTION: The diagram show a square - shaped lawn with 6 m by 8 m pool built inside. A) Find an equation expressing the area of the lawn in terms of the side length, x, of the shape.

Question 1181359: The diagram show a square - shaped lawn with 6 m by 8 m pool built inside.
A) Find an equation expressing the area of the lawn in terms of the side length, x, of the shape.
B) State its domain and range.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A) The lawn is a square with side length x (meters), with a pool 6m x 8m somewhere in the lawn. The area of lawn is the area of the square, minus the area of the pool.

ANSWER: The equation for the area of lawn in square meters is

The minimum value for x, the length of a side of the square, is the longer dimension of the pool.
There is no maximum value for the side length of the square.
ANSWER: The domain is [8,infinity)

The minimum area of lawn is when the side length of the square is minimum -- that is, when x=8. The minimum area is then 8^2=64-48=16.
There is no maximum for the area.
ANSWER: The range is [16,infinity)

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