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 is:

Options

• 6 cm

• 4.5 cm

• 3 cm

• 5.25 cm

Answer 1

3 cm

Explanation:

Given, PQ || XY || BC

AP = 2 cm

PX = 1.5 cm

BX = 4 cm

QY = 0.75 cm

In AAXY by,

Using BPT ΔΑΧΥ,

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

`2/1.5 = (AQ)/0.75`

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

= 2 × 0.5

= 1 cm

In AABC by using Thale’s theorem,

`(AX)/(XB) = (AX)/(CY)`

`(AP + PX)/(XB) = (AQ + QY)/(CY)`

`(2 + 1.5)/4 = (1 + 0.75)/(CY)`

`3.5/4 = 1.75/(CY)`

CY = `7.0/3.5`

CY = 2 cm

Then, AQ + CY

= 1 + 2

= 3 cm