Question

How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?

A. 11 m
B. 4 m
C.
D.

Answer 1

10.246 or sqrt(105)

Explanation:

Given,

length of the ladder = 11 m

distance of the foot of the ladder from the base of the wall = 4 m

According to Pythagoras' theorem,

(hypotenuse)^2 = (side1)^2 + (side2)^2

As per the problem,

hypotenuse = 11m

side1 = distance from wall = 4 m

side2 = height reached by the ladder on the wall

that is, (11)^2 = (4)^2 + (side2)^2

121 = 16 + (side2)^2

121 - 16 = (side2)^2

(side2)^2 = 105

(side2) = sqrt(105) = 10.246 m

Hence, the ladder can reach up to 10.246 m height on the wall.

Answer 2

√105 meters, or about 10.25 meters

Explanation:

`{x}^(2) + {4}^(2) = {11}^(2)`

`{x}^(2) + 16 = 121`

`{x}^(2) = 105`

`x = √(105) = 10.25`