Question

The length of a ladder is exactly equal to the height of the wall it is leaning 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

• A. 12 m
• B. 15 m
• C. 18 m
• D. 11 m

Hint:

When an object is raised on a platform, reduce the total vertical distance by platform height in Pythagoras.

Answer 1

The Correct Option is B

Let height of wall = length of ladder = $h$. From the stool top to the wall top: vertical height = $h - 3$, horizontal distance = 9 m. Using Pythagoras: \[ (h - 3)^2 + 9^2 = h^2 \] \[ h^2 - 6h + 9 + 81 = h^2 \] \[ -6h + 90 = 0 \Rightarrow h = 15 \ \text{m}. \] % Quick tip