Ramu observed that in order toclimb a 12 meter high wall, he requires either a 13meter or a 20 meter long ladder if he keeps them at distances of x and y respectively from the foot of the wall assume that the ladders just touch the top of the wall what is the value of x + y?

21 meters

Step-by-step explanation:

Step 1 :

Let x be the distance at which the 13 meter ladder is placed . We can consider this as a triangle with one angle as 90°, where the ladder is the hypotenuse and the wall is one side. We need to find the 3rd side  x.

Using Pythagoras theorem, we have

13² = 12² + x² => 169 = 144 + x² => x² = 169-144 = 25

=> x = 5 meters

Step 2 :

Similarly ,

Let y be the distance at which the 20 meter ladder is placed . We can consider this as a triangle with one angle as 90°, where the ladder is the hypotenuse and the wall is one side. We need to find the 3 rd side which is y.

Using Pythagoras theorem, we have

i.e  20² = 12² + y² => 400 = 144 + y² => y² = 200-144 = 256

=> y = 16 meters

Step 3 :

Value of x + y  = 5 + 16 = 21 meters