Question

A 20m ladder and a 15m ladder were leaned against a building. The bottom of the longer ladder was 7m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find this distance.

6m

12m

10m

9m

Answer 1

The correct answer is: d=9m

Explanation:

Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.

Then, using the Pythagorean Theorem we have:

20m ladder:

20^2 = h^2 + (d+7)^2 (Eq. 1)

400 = h^2 + d^2 + 2*7*d + 7^2 (expanding the theorem)

400 = (h^2 + d^2) + 14*d + 49 (Eq. 2)

15m ladder:

15^2 = h^2 + (d)^2 (Eq. 3)

Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):

400 = (15^2) + 14*d + 49

400 = 225 + 14*d + 49

14*d = 400 - 225 - 49 (clearing the variable d)

14*d = 126

d = 9 m

And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.

And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building