Question

Quadratic Equations. Please help

Answer 1

Answer:

• maximum area: 1250 square units
• width: 50 units
• length: 25 units

Step-by-step explanation:

The area is the product of the width and length. Using the given expressions, we find the area to be ...

  A = LW

  A = (x)(100 -x)/2

We note this is a quadratic with zeros at x = 0 and x = 100, values that make the factors zero. The maximum will be at the vertex of the graph, on the line of symmetry, halfway between the zeros: x = (0 +100)/2 = 50.

a)

The maximum area will be for x=50.

  A = (50)(100 -50)/2 = 2500/2 = 1250 . . . . square units

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b)

The width was found in the above discussion. The width for maximum area is 50 units.

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c)

The length for maximum area can be found from the length expression:

  (100 -50)/2 = 50/2 = 25

The length for maximum area is 25 units.

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As defined by the problem statement, x in the attached graph is the width of the rectangle.