Answer:
The correct answer is: d=9m
Step-by-step 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
