A kennel owner has 400 feet of fencing to enclose a rectangular dog exercise pen. Express the area of the exercise pen, A, as a

Question

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A kennel owner has 400 feet of fencing to enclose a rectangular dog exercise pen. Express the area of the exercise pen, A, as a

function of one of its dimensions, x. A(x) = x(x - 200) A(x) = x(x - 200) A(x) = x(400 - x) A(x) = x(400 - x) A(x) = x(200 - x) A(x) = x(200 - x) A(x) = (200 - x)2

Mathematics

1 answer:

DENIUS [597] · Answer 1 · 2022-03-14T04:20:38+03:00

Answer:

A(x) = x(200-x)

Step-by-step explanation:

400 feet of fencing to enclose a rectangular dog exercise pen means the perimeter of rectangle is 400 feet

If x is length and y is breadth. Perimeter is given by :

P = 2(x+y)

400 = 2(x+y)

⇒ (x+y) = 200 .....(1)

y = 200-x

Area of a rectangle is given by :

A = xy

A(x) = x(200-x)

Hence, the area as a function of length of rectangle is x(200-x).