Question 70

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

Solution

Let height of ladder be $$AD=h$$ m, => AE = $$(h-3)$$ m and ED = 9 m

In right $$\triangle$$ ADE,

=> $$(AD)^2=(AE)^2+(ED)^2$$

=> $$(h)^2=(h-3)^2+(9)^2$$

=> $$h^2=h^2-6h+9+81$$

=> $$6h=90$$

=> $$h=\frac{90}{6}=15$$

$$\therefore$$ Length of ladder = Height of wall = 15 m

=> Ans - (A)

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