Question

walls of two buildings on either side of a street are parallel to each other, a ladder 5.8m long is placed on the street such that its top just reaches the window of a building at the height of 4m on turning the ladder over to the other side of the street its top touches the window of the other building at a height of 4.2m. Find the width of the street?

Answer 1

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Answer 2

Answer:

The width of street is 8.2 m.

Step-by-step explanation:

We are given that the two buildings are parallel to each other

Refer the attached figure .

So, AB is parallel to ED

Since we are given that a ladder 5.8m long is placed on the street such that its top just reaches the window of a building at the height of 4m

So. AC = EC = 5.8 m

And AB = 4 m.

On turning the ladder over to the other side of the street its top touches the window of the other building at a height of 4.2m.

So, ED = 4.2 m

So, let BC = x and CD = y

We are required to calculate the width of street i.e. x+y

So, in ΔABC , use Pythagorean Theorem

$Hypotenuse^{2} =Perpendicular^{2}+ Base^{2}$

$AC^{2} =AB^{2}+ BC^{2}$

$5.8^{2} =4^{2}+ x^{2}$

$33.64 =16+x^{2}$

$33.64 -16 =x^{2}$

$17.64  =x^{2}$

$\sqrt{17.64}=x$

$4.2=x$

So, in ΔEDC , use Pythagorean Theorem

$Hypotenuse^{2} =Perpendicular^{2}+ Base^{2}$

$EC^{2} =ED^{2}+ DC^{2}$

$5.8^{2} =4.2^{2}+ y^{2}$

$33.64 =17.64+y^{2}$

$33.64 -17.64 =y^{2}$

$16 =y^{2}$

$\sqrt{16}=y$

$4=y$

So, the width of street = x+y = 4.2+4 =8.2 m

Hence the width of street is 8.2 m.