A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth.
A) CA = CB = 6 ft, CM = 3 ft.
B) CA = CB = 4 ft, CM = 4 ft.
C) CA = CB = 8 ft, CM = 8 ft.
D) CA = CB = 2 ft, CM = 2.83 ft.
E) CA = CB = 4 ft, CM = 8 ft.

Question

A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth. 
A) CA = CB = 6 ft, CM = 3 ft. 
B) CA = CB = 4 ft, CM = 4 ft. 
C) CA = CB = 8 ft, CM = 8 ft. 
D) CA = CB = 2 ft, CM = 2.83 ft. 
E) CA = CB = 4 ft, CM = 8 ft.

Quizplus · Accepted Answer

Since the diameter of the boiler is 4 ft, the radius of the boiler is 2 ft. Drawing a line from the center of the boiler M to the corner C creates a right triangle with legs CM and the distance from the corner to either point A or B. Using the Pythagorean theorem, we have:

$$(	ext{distance from corner to point A or B})^2 = CM^2 + (2	ext{ ft})^2$$

$$= 4 + 4 = 8$$

$$	ext{distance from corner to point A or B} = \sqrt{8} \approx 2.83 	ext{ ft}$$

Therefore, the answer is D since both CA and CB are 2.83 ft and CM is 2 ft.

A Boiler 4 Ft in Diameter Is to Be Placed