Question

a ladder 50dm long is placed so as to reach a window 48 dm high and on turning the ladder over to the other side of the street it reaches a point 14dm high. find the breadth of the street.​

Answer 1

Answer:

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Answer 2

The breadth of the street is 62 dm.

Given:

• A ladder 50dm long is placed so as to reach a window 48 dm high and on turning the ladder over to the other side of the street it reaches a point 14dm high.

To find:

• Find the breadth of the street.

Solution:

Concept to be used:

• Draw the situation.
• Apply Pythagorus theorem.

Step 1:

Find the length of BE.

Apply the Pythagoras theorem in ∆ABE.

$AE ^{2} =AB^{2} +BE^{2}$

${(50)}^{2} = ( {48)}^{2} + {BE}^{2}$

$2500 = 2304 + {BE}^{2}$

$BE^{2} = 196$

$BE =\pm 14$

Ignore the (-)ve value.

Thus,

$\bf BE = 14 \: dm$

Step 2:

Find the length of ED.

$EF ^{2} = FD^{2} +ED^{2}$

$( {50)}^{2} = ( {14)}^{2} + ED^{2}$

$ED^{2} = 2500 - 196$

$ED^{2} = 2304$

$ED = \pm 48$

Ignore the (-)ve value.

Thus,

$\bf ED = 48 \: dm$

Step 3:

Find the breadth of street.

Breadth of street $\bf BD= BE+ED$

$BD= 14 + 48$

$\bf BD= 62 \: dm$

Thus,

The breadth of street is 62 dm.

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