A ladder 15m long reaches a window which is 9m above the groubd on one side of the street. Keeping its foor at the same point, the ladder is turned to the other side of the street to reach a window 12m high. The width of the street is ______ meter?
Length of ladder=AC=15m
Height of window from ground
in first case AB=9m
ABC is right angled triangle
Ac^2=AB^2+BC^2
BC=12m
In second case
Let CE be length of ladder=15m
Height of window from ground=DE=12m
Triangle CDE is a right angled triangle
CE^2=DE^2+CD^2
CD=9m
Width of street=BC+CD=9+12=21m
21
Remember your basic 3-4-5 right triangle. Scale it up by 3 and you have 9-12-15.
Now draw your diagram, and all should be clear.
To find the width of the street, we can use the concept of similar triangles. Let's consider the situation:
On one side of the street, the ladder forms a right-angled triangle with the ground and the window. The ladder is the hypotenuse, which is 15m, and the height of the window is 9m.
On the other side of the street, the ladder forms a similar right-angled triangle with the ground and the new window. The height of the new window is 12m.
Since the two triangles are similar, their corresponding sides have a proportional relationship. Therefore, we can set up the following proportion:
(Width of the street)/(9m) = (Width of the street + 15m)/(12m)
To solve for the width of the street, we can cross-multiply and solve the equation:
12m * (Width of the street) = 9m * (Width of the street + 15m)
12m * Width of the street = 9m * Width of the street + 135m^2
12m * Width of the street - 9m * Width of the street = 135m^2
3m * Width of the street = 135m^2
Divide both sides by 3m:
Width of the street = 135m^2 / 3m
Simplifying:
Width of the street = 45m
Therefore, the width of the street is 45 meters.