Question

Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, the distance between their tops is: 6 मीटर और 11 मीटर की ऊँचाई वाले दो खंभे समतल जमीन पर खड़े हैं। अगर उनके नीचे यदि सिरों के बीच की दूरी 12 मीटर है, तो उनके ऊपरी सिरों के बीच की दूरी होगी: *
14 ਮੀ: (m)(मी.)
12 ਮੀ: (m) (मी.)
13 ਮੀ: (m) (मी.)
11 ਮੀ: (m) (मी.)
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Answer 1

Answer :–

To Find :-

The length of Distance between the top of the poles.

Given :-

• Length of first pole (DC) = 6 m.

• Length of second pole (AB) = 11m.

• Distance between the bottom of the poles = 12 m.

We know :-

⠀⠀⠀⠀⠀⠀⠀Pythagoras theorem :-

$\boxed{\bf{H^{2} = B^{2} + P^{2}}}$

Where :-

• H = Hypotenuse

• B = Base

• P = Height

Concept :-

According to the Question and the diagram , we get the values as :-

• DC = FB = 6 m

• DF = CB = 12 m

• FB = AB - FB

⠀⠀⠀⠀⠀⠀⠀==> FB = (11 - 6) m

⠀⠀⠀⠀⠀⠀⠀==> FB = 5 m

Hence, we get the values in the ∆ AFD as :-

• Height = 5 m

• Base = 12 m

Now , we can use the Pythagoras theorem to determine the Hypotenuse of the triangle.

And as we know the Hypotenuse of the triangle is the distance between the top of the two poles.

Solution :-

⠀⠀⠀⠀⠀The Distance between the ⠀⠀⠀⠀⠀⠀⠀⠀⠀top of the two poles :-

Given :-

• B = 12 m

• H = 5 m

Let the Hypotenuse be x m.

Using the Pythagoras theorem and substituting the values in it , we get :-

$:\implies \bf{H^{2} = B^{2} + P^{2}} \\ \\ \\ :\implies \bf{x^{2} = 12^{2} + 5^{2}} \\ \\ \\ :\implies \bf{x = \sqrt{12^{2} + 5^{2}}} \\ \\ \\ :\implies \bf{x = \sqrt{144 + 25}} \\ \\ \\ :\implies \bf{x = \sqrt{169}} \\ \\ \\ :\implies \bf{x = 13} \\ \\ \\ \therefore \purple{\bf{Hypotenuse = 13 m}}$

Hence, the Hypotenuse of the triangle is 13 m.

But as we know the length DB is the Distance between the top of the poles , we get :-

The distance between the top of the poles is 13 m