In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm. Find: XY - Noon Academy

In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm. Find: XY

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

In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm. Find: XY

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 1

Solution:

According to the given question,

$XY\text{ }||\text{ }BC$

So, In

$\Delta \text{ }AXY\text{ }and\text{ }\Delta \text{ }ABC$

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

[Corresponding angles]

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

[Corresponding angles]

Hence,

$\vartriangle AXY\text{ }\sim\text{ }\vartriangle ABC\text{ }by\text{ }AA$

criterion for similarity.

As corresponding sides of similar triangles are proportional, we have

As,

$\vartriangle AXY\text{ }\sim\text{ }\vartriangle ABC$

$AX/AB\text{ }=\text{ }XY/BC$

$9/13.5\text{ }=\text{ }XY/18$

Or,

$XY\text{ }=\text{ }\left( 9\text{ }x\text{ }18 \right)/\text{ }13.5\text{ }=\text{ }12\text{ }cm$

i

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