Question

Two electric poles are erected on the ground. The height of the poles is 20 m and 28 m respectively. The distance between the poles is 15 m. To join the top of the poles, how much wire will be required ?

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Answer 1

Given :-

• Two electric poles are erected on the ground.

• The height of the poles is 20 m and 28 m respectively.

• The distance between the poles is 15 m.

To Find :-

• To join the top of the poles, how much wire will be required ?

Solution :-

Let us assume that AB and CD be the two electric poles such that

• AB = 20 m

• CD = 28 m

• AC = 15 m

From B, draw BE perpendicular on CD, intersecting CD at E.

So,

• BE = AC = 15 m

and

• AB = CE = 20m

Also,

• DE = CD - CE = 28 - 20 = 8 m.

Now,

$\rm :\longmapsto\:In \: \triangle \: BDE$

Using Pythagoras Theorem,

$\rm :\longmapsto\: {BD}^{2} = {BE}^{2} + {DE}^{2}$

$\rm :\longmapsto\: {BD}^{2} = {15}^{2} + {8}^{2}$

$\rm :\longmapsto\: {BD}^{2} = 225 + 64$

$\rm :\longmapsto\: {BD}^{2} = 289$

$\bf :\longmapsto\: {BD} = 17 \: m$

Hence,

To join the top of two poles, 17 m wire is required.

Additional Information :-

1. Pythagoras Theorem :-

• This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

• This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

• This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem,

• If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

Answer 2

Answer:

Given :-

Two electric poles are erected on the ground.

The height of the poles is 20 m and 28 m respectively.

The distance between the poles is 15 m.

To Find :-

To join the top of the poles, how much wire will be required ?

Solution :-

Let us assume that AB and CD be the two electric poles such that

AB = 20 m

CD = 28 m

AC = 15 m

From B, draw BE perpendicular on CD, intersecting CD at E.

So,

BE = AC = 15 m

and

AB = CE = 20m

Also,

DE = CD - CE = 28 - 20 = 8 m.

Now,

\rm :\longmapsto\:In \: \triangle \: BDE:⟼In△BDE

Using Pythagoras Theorem,

\rm :\longmapsto\: {BD}^{2} = {BE}^{2} + {DE}^{2}:⟼BD

2

=BE

2

+DE

2

\rm :\longmapsto\: {BD}^{2} = {15}^{2} + {8}^{2}:⟼BD

2

=15

2

+8

2

\rm :\longmapsto\: {BD}^{2} = 225 + 64:⟼BD

2

=225+64

\rm :\longmapsto\: {BD}^{2} = 289:⟼BD

2

=289

\bf :\longmapsto\: {BD} = 17 \: m:⟼BD=17m

Hence,

To join the top of two poles, 17 m wire is required.

Additional Information :-

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem,

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

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