In the given figure, Δ ABC ~ Δ ADE. If AE: EC = 4: 7 and DE = 6.6 cm, find BC. If ‘x’ be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of ‘x’. - Noon Academy

In the given figure, Δ ABC ~ Δ ADE. If AE: EC = 4: 7 and DE = 6.6 cm, find BC. If ‘x’ be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of ‘x’.

Class 10 | Exercise 15B | ICSE | Maths | Selina | Similarity (With Applications to Maps and Models)

In the given figure, Δ ABC ~ Δ ADE. If AE: EC = 4: 7 and DE = 6.6 cm, find BC. If ‘x’ be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of ‘x’.

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(B) - 6

Solution:

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(B) - 7

According to the given question,

$\Delta \text{ }ABC\text{ }\sim\text{ }\Delta \text{ }ADE$

So, we have

$AE/AC\text{ }=\text{ }DE/BC$

$4/11\text{ }=\text{ }6.6/BC$

Or,

$BC=\left( 11\text{ }x\text{ }6.6 \right)/4=18.15cm$

And, also

$\Delta \text{ }ABC\text{ }\sim\text{ }\Delta \text{ }ADE$

we have

$\angle ABC\text{ }=\angle ADE$

And

$\angle ACB\text{ }=\angle AED$

So,

$DE\text{ }||\text{ }BC$

And,

$AB/AD\text{ }=\text{ }AC/AE\text{ }=\text{ }11/4$

$\left[ Since,\text{ }AE/EC\text{ }=\text{ }4/7 \right]$

In

$\vartriangle \text{ }ADP\text{ }and\text{ }\vartriangle \text{ }ABQ$

$\angle ADP\text{ }=\angle ABQ$

[As DP || BQ, corresponding angles are equal.]

$\angle APD\text{ }=\angle AQB$

[As DP || BQ, corresponding angles are equal.]

So,

$\vartriangle ADP\text{ }\sim\text{ }\vartriangle ABQ\text{ }by\text{ }AA$

criterion for similarity

$AD/AB\text{ }=\text{ }AP/AQ$

$4/11\text{ }=\text{ }x/AQ$

Hence,

$AQ\text{ }=\text{ }\left( 11/4 \right)x$

i

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