Question

solve it fast...... ​

Answer 1

Given:

• XY || RQ
• PX = 1 cm
• QX = 3 cm
• YR = 4.5 cm.
• QR = 9 cm

To find:

PY, XY

Method

By Basic proportionality theorem or Thales theorem,

$\sf{ \frac{PX}{XQ} = \frac{PY}{YR} }$

$\implies \frac{1}{3} = \frac{PY}{4.5}$

On cross multiplication,

⇒ 3 PY = 4.5

⇒ PY = 1.5 cm

In ∆ PXY and ∆ PQR, XY is parallel to QR, so corresponding angles are equal.

∠PXY=∠PQR

∠PYX=∠PRQ

Hence, △PXY∼△PQR [By AA similarity criterion]

$\sf{ \frac{PX}{PQ} = \frac{XY}{QR} }$

$\implies \frac{1}{4} = \frac{XY}{9}$

On cross multiplication,

4 XY = 9

∴XY = 2.25 cm