Question

A person decides to build a horse corral using a barn for one side. Has has 30m of fencing materials and wants the corral to have an area of 100m ^ 2 . What are the dimensions of the corral?

Answer 1

Two possible answers:

• A 10 m by 10 m corral
• A 5 m by 20 m corral

See the diagrams below.

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Explanation:

x = length

y = width

Let side x be parallel to the barn wall. This means we have 1 copy of x and 2 copies of y to form this partial rectangle. The fourth side is the barn itself, so we don't need this as the fencing.

The perimeter of the fencing is x+y+y = x+2y

Set this equal to the 30 meters of fencing and solve for x.

x+2y = 30

x = -2y+30

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area = length*width

area = x*y

area = (-2y+30)*y

area = -2y^2+30y

Set this equal to the given area of 100 m^2 and solve for y

-2y^2+30y = 100

-2y^2+30y-100 = 0

-2(y^2-15y+50) = 0

y^2-15y+50 = 0

(y-10)(y-5) = 0

y-10 = 0 or y-5 = 0

y = 10 or y = 5

Side note: The quadratic formula is an alternative path you can take.

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If y = 10, then x would be...

x = -2y+30

x = -2*10+30

x = -20+30

x = 10

This produces a 10 meter by 10 meter enclosure.

Or, if y = 5, then,

x = -2y+30

x = -2*5+30

x = -10+30

x = 20

The corral is 5 by 20 in this case.

Unfortunately there are two possible answers. Without more info, we cannot nail down which one to go with.

The diagram of each is shown below.