1 October, 03:37

# The management of a large store has 1,600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining three sides, find the area of the largest possible yard.

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Answers (1)
1. 1 October, 06:44
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The largest area of the yard is = 320000 ft²

Step-by-step explanation:

Management has 1600 ft of fencing

They are going to build a rectangular storage (using a building wall as one of the side)

We will find the largest possible yard

Lets call

y the largest side of the rectangle

x the smaller side of the rectangle

Then we have:

Area of rectangle A = x*y

Perimeter of the rectangle (notice one side will be of wall)

P = 1600 ft P = 2x + y y = P - 2x y = 1600-2x

Then

A (x) = x * (1600 - 2x) A (x) = 1600*x - 2x²

So A' (x) = 1600 - 4x A' (x) = 0 1600 - 4x = 0 x = 400 ft

and y = (1600-2*x) ⇒ y = 800 ft

The largest yard is = x * y = 400*800 = 320000 ft²
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