A20m 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

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

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.