Question

The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft

Answer 1

Apply the Pythagorean theorem

a^2 + b^2 = c^2

a = 5, b = 13.

5^2 = 25, 13^2 = 169

25 + 169 = 194

square root 194 = 13.928, rounded to nearest foot = 14 ft. 

The minimum ladder length required to reach the top of the wall = 14 ft. 
  

Answer 2

Answer:

C) 14 ft

Step-by-step explanation:

Let l be the length of ladder ,

The distance of ladder from the wall = 13 ft,

And, the height of wall = 5 ft,

Since, the length of ladder is minimum when the wall is straight,

In this condition,

$l^2=(\text{The distance of ladder from the wall})^2+(\text{Height of wall})^2$

$\implies l^2=13^2+5^2$

$\implies l^2 = 169 + 25 = 194$

$\implies l=13.9283883\approx 14$

Hence, the approximate minimum length of the ladder is 14 ft.