Jamaal’s pit-bull (Walter) has a 9.78m long leash tethered to the corner of his equilateral triangle pit-bull mansion. How much outdoor territory can Walter mar

Question

How much outdoor territory can Walter mark based on the given information.

Answer 1

Okay first off Walter the Pit-bull should be rescued because a triangular doghouse has no roof. 

 

Second, forget the triangle. This problem is about a length moving around a point. That is totally a circle!

 

Its radius is 9.78m, so you just put that in the area equation for a circle to get the area, errr the "outdoor territory"

 

pi* (9.78)^2

 

 

Answer 2

Assuming the side lengths of the equilateral

triangular shaped doghouse are small enough

to allow the dog to encompass the doghouse in

it's travels... the area he can mark outside

of the doghouse is the area of the circle

as prescribed by a radius of 9.78m minus

the area of the triangular doghouse.

 

Area of circle:  πr² = 3.14(9.78)² = 300.336 m²

 

For the triangle:

Area = (1/2)bh

Let x represent the length of a side of the doghouse in meters

 

The height can be found by use of Pythagorean theorem

Cutting the base in half to create two right triangles:

h² + (0.5x)² = x²

h² + 0.25x² = x²

h² = 0.75x²

h = (√.75)x

h = 0.866x

 

Area = (1/2)(x)(.866x) = .866x²/2 = 0.433x²

 

The outside area the dog can mark is:

300.336 - 0.433x² square meters