Question about triangles

Question

If Victa the goat is tied to a pole at 1 corner of a square paddock with a length of a side being 24m, what length must the rope be for Victa to graze half the paddock?

Answer 1

To solve this question, let's first calculate the Area the goat will graze, which will be 1/2 of 24m x 24m, or 288m².

 

A rope will permit the goat to graze a portion of a circle, in this case, 1/4 of a circle.  The Area of that portion of the circle will be 288m².

 

The Area of the circle will be 288m² x 4 = 1,152m².

 

We then need to determine the radius of a circle which has an Area of 1,152m².

 

So, 1,152m² = pi x R², which yields √(1,152m²/pi) = 19.1m

Answer 2

Draw a diagram!

 

The area of the square is 24² or 576 m².

Half of that area is 288 m²

Victa shall graze an area in the shape of quarter of a circle

 

(0.25)πr² = 288          divide both sides by 0.25

πr² = 1152                  divide both sides by π

r² ≈ 366.92989          take square root of both sides

r ≈ 19.1554141

 

The rope should be 19.2 m.