Question

Question : The diagram shows a plan for creating a zoo’s elephant exhibit. The elephant pen will be surrounded on two sides by a walkway with a viewing area in one corner. The sides, shown as dotted lines, will be fenced. How much fencing separates the elephant area from the walkways

answer choices :

(A) 180 feet
(B) 250 feet
(C) 540 feet
(D) 750 feet

Answer 1

C

Explanation:

We need to find the length of the red dotted line.

It is divided into 3 parts: the top, the middle slant, and the bottom

The top

Goes from y = 50 to y = 120, the length is:

120 - 50 = 70 units

The bottom

Goes from x = 60 to x = 120, the length is:

120 - 60 = 60 units

The middle slant

This is hypotenuse of the right triangle shown.

We will use Pythagorean Theorem to solve for this length, let it be x.

The theorem is:

Leg^2 + Another Leg^2 = x^2

One leg goes from x = 20 to x = 60, the length is 60 - 20 = 40

Another leg goes from y = 20 to y = 50, the lenth is 50 - 20 = 30

So, we have:

`30^2+40^2=x^2\\2500=x^2\\x=√(2500)\\x=50`

THe slant length is 50 units

TOtal fencing is: 70 + 60 + 50 = 180 units

1 unit is 3 feet, so

180 units * 3 = 540 feet

C is the correct answer