Question

In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY = ______.

Options

• 6 cm

• 4.5 cm

• 3 cm

• 5.25 cm

Answer 1

In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY = 3 cm.

Explanation:

Given:

PQ || XY || BC

AP = 2 cm

PX = 1.5 cm

BX = 4 cm

QY = 0.75 cm

We need to find AQ + CY

find AQ
Since PQ || BC, triangles are similar, and we use the property of proportionality:

`(AQ)/(AP) = (QY)/(PX)`

`(AQ)/2 = (0.75)/(1.5)`

AQ = `2 xx (0.75)/(1.5)`

= 2 × 0.5

= 1 cm

find CY

Using the same proportionality:

`(CY)/(BX) = (QY)/(PX)`

`(CY)/4 = (0.75)/(1.5)`

CY = `4 xx (0.75)/(1.5)`

= 4 × 0.5

= 2 cm

AQ + CY = 1 + 2

= 3 cm