SOLUTION: Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x

SOLUTION: Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units? a. square b. rectangle

Question 807497:
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
a.
square
b.
rectangle

Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
a.
square area = sq units
b.
rectangle area = sq units

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

For a given perimeter, a square is the greatest area rectangle that can be constructed. so your square and rectangle have the same perimeter.

so

Since area is length times width

Since this is a quadratic function with a negative lead coefficient, the graph is a downward-opening parabola, hence the function value at the vertex represents a maximum value of the function.

The independent variable () coordinate of the vertex is:

Therefore the maximum area is obtained when the width of the rectangle is the perimeter divided by 4. If the perimeter divided by 4 is the width, 2 times the width is the perimeter divided by 2, and then 2 times the length must also be the perimeter divided by 2. The four sides are equal in measure, and the maximum area figure is a square.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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