Question

In figure, XY║BC and AX:XB = 1:3. The length of XY is

Answer 1

Answer:

Hence, the value of XY = 1.5 cm

Answer 2

Given:

In figure, XY║BC and AX:XB = 1:3. The length of XY is?

To find:

The length of XY

Solution:

XY║BC (given)

So, in Δ AXY and Δ ABC, we have

∠XAY = ∠BAC . . . [common angles]

∠AXY = ∠ABC . . . [corresponding angles]

∴ Δ AXY ~ Δ ABC . . . [By AA similarity]

We know that,

The corresponding sides of two similar triangles are proportional to each other.

Therefore,

$\frac{AX}{AB} = \frac{XY}{BC}$

$\implies \frac{AX }{AX + XB} = \frac{XY}{BC}$

on substituting the values of AX = 1 cm, XB = 3 cm and BC = 6 cm from the figure, we get

$\implies \frac{1 }{1 + 3} = \frac{XY}{6}$

$\implies \frac{1 }{4} = \frac{XY}{6}$

$\implies XY = \frac{6 }{4}$

$\implies XY = \frac{3 }{2}$

$\implies \bold{XY = 1.5\:cm}$

Thus, the length of XY is → 1.5 cm.

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Also View:

If in the figure, XY || BC, AX = 9 cm, XB = 7 cm, and BC = 20 cm, then XY?

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Observe the figure and state whether line XY is parallel to side BC. give your reason​

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