Question

Two poles of height 12 m and 24 m are standing on the ground. If the distance between their tops is 20 m, find the distance between their feet.

Answer 1

• The distance between their feet is equal to 16 m .

Given :- (from image)

• ED (Pole) = 12 m
• AC (Pole) = 24 m
• AE = The distance between their tops = 20 m .

To Find :-

• The distance between their feet = DC = ?

Solution :-

from image we can see that,

→ ED = 12 m

and,

→ AC = 24 m

Construction :- Join EB .

So,

→ ED = BC = 12 m

then,

→ AB = AC - BC

→ AB = 24 - 12 = 12 m .

now, in right angled ∆ABE we have,

→ AB = Perpendicular = 12 m

→ AE = Hypotenuse = 20 m .

then,

→ EB = √[(AE² - AB²)] { By pythagoras theorem }

→ EB = √(20² - 12²)

→ EB = √(400 - 144)

→ EB = √(256)

→ EB = 16 m .

therefore,

→ DC = EB

→ DC = 16 m (Ans.)

Hence, the distance between their feet is equal to 16 m .

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Answer 2

Given:

Two poles of height 12 m and 24 m are standing on the ground. If the distance between their tops is 20 m

To Find:

Find the distance between their feet

Solution:

Let us first draw a diagram so that we can visualise the question more easily, construct two lines one shorter and one bigger and label them as 12 and 24, now we can see that the distance between tops is 20m and also that the distance BC and AE is equal as AB and CD are parallel to each other so in the triangle DEA,

AD=20m

AE=x

DE=24-12=12m

Now applying the Pythagoras theorem to find the value of AE, we have

$AD^2=AE^2+DE^2\\20^2=x^2+12^2\\x^2=20^2-12^2\\x=\sqrt{400-144}\\x=\sqrt{256}\\x=16m$

So the value of x is 16m which is AE and AE is equal to BC, so the distance between their feet is 16m

Hence, the distance between their feet is 16m.