Question

A dog is attached to a 49 foot rope fastened to the outside corner of a fenced-in garden that measures 42 feet by 51 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.

Answer 1

5698 sq. cm is the answer.

Explanation:

Since dog cannot enter the garden therefore and it can wander as maximum as its rope can move which actually makes a circle. therefore it makes 3rd fourth of circle with radius 49 cm and then one fourth part circle with radius 7 cm with another corner ( From the corner 42 foot away from where the leash begins ,the dog has only 49 - 42 = 7 foot of leash left )

So total area covered by dog =
`(3)/(4) \pi {(49)}^2` +

`(1)/(4) \pi {(7)}^2`

=
`(49)/(4) \pi [49(3) + 1]`

=
`(49)/(4) \pi (148)`

= 37 (49) (
`(22)/(7)`

= 37x7x22

=5698 sq cm

Answer 2

Assuming that the corner of the fence has right angle, the the area that the dog wandered will be given by:
A=θ/360πr²
Where:
θ=360-90=270°
r=49 ft
hence the area will be:
A=270/360×π×49²
A=5657.23 ft²
Thus the dog will wander in the area of 5657.23 ft²