A ladder of 15 m length reaches a window of a house which is 12 m above the ground on one side of the street. Keeping the foot of the ladder at the same point it is turned to the other side of the street and now it reaches the window of some other house which is 9 m high. The width of street is :
Question
A ladder of 15 m length reaches a window of a house which is 12 m above the ground on one side of the street. Keeping the foot of the ladder at the same point it is turned to the other side of the street and now it reaches the window of some other house which is 9 m high. The width of street is :
Solution
To find the width of the street, we can use the concept of similar triangles.
Let's denote the width of the street as 'x'.
On one side of the street, the ladder forms a right triangle with the ground and the window. The ladder is the hypotenuse, which is 15 m, and the height of the window is 12 m.
Using the Pythagorean theorem, we can find the length of the base of this triangle (the distance from the foot of the ladder to the window).
So, we have:
(base)^2 + (height)^2 = (hypotenuse)^2 x^2 + 12^2 = 15^2 x^2 + 144 = 225 x^2 = 225 - 144 x^2 = 81 x = √81 x = 9
Therefore, the width of the street is 9 meters.
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