A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall

By the rule of Pythagoras Theorem,

Pythagoras theorem states that for any right angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of square on the legs.

In the above figure RQ is the hypotenuse,

15² = 12² + a²

225 = 144 + a²

By transposing 144 from RHS to LHS it becomes – 144

a² = 225 – 144

a² = 81

a = √81

a = 9 m

Hence, the length of a = 9 m.