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The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height $3$ m and the stool is kept $9$ m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is:

1. $12$m
2. $15$m
3. $18$m
4. $11$m

• Let the length of the ladder  be X   and length of the wall be L ( perp.)
• Lower end of the ladder is kept on a stool of height 3m.
• 9m is the base and X - 3 is the length of the ladder after removing height of the stool( Hypot.)
• ( L , X - 3 , 9 ) form a Pythagorean triplet.
•  L = X + 3 (The length of a ladder is exactly equal to the height of the wall it is resting against.)

I think it will be clear from now on what type of Pythagorean triplet we are looking for.
On in which 9 is a side other than hypotenuse (longest side) and difference between the sides is 3m.
Yes, that is (9, 12, 15). So length of ladder is 15m(longest side).

and the length of the wall = 12 m

Option A is the Correct Answer.

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