Question

A rope is stretched from the top of a 6-foot tent to a point on the

ground that is 11 feet from the base of the tent.
6 ft
11 ft
How long is the rope? Approximate to the nearest tenth if necessary.
A. 12.5 ft
O B. 5 ft
5
O C. 17 ft
D. 9.1 ft

Answer 1

A. 12.5 ft

Explanation:

The geometry is modeled by a right triangle with legs 6 ft and 11 ft. The length of the rope is the length of the hypotenuse of that triangle. That is given by the Pythagorean theorem:

c² = a² +b² . . . . . . where c is the hypotenuse and a, b are the leg lengths

c = √(a² +b²) = √(6² +11²) = √(36 +121) = √157

c ≈ 12.530 . . . . feet

The rope is about 12.5 feet long.

_____

Additional comment

The hypotenuse of a right triangle is longer than either leg, and is shorter than the sum of the two legs. That means ...

11 < c < 17

Only one answer choice fits.