Question

XY is drawn parallel to the base BC of a $\triangle ABC$ cutting AB at X and AC at Y. If AB = 4 BX and YC = 2 cm, then AY =
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Answer 1

Answer:

The Length of AY is 6 cm.

Among the given options option (c) is 6 cm is the correct answer.

Step-by-step explanation:

Given:

XY || BC in ΔABC, cutting AB at X and AC at Y.

AB = 4 BX & YC = 2 cm.

 

In ΔAXY and ΔABC,  

∠ AXY = ∠ B       (corresponding angles)

∠ A = ∠ A              (common)

ΔABC ~ ΔAXY [By AA Similarity criterion

 

AB = AX + BX

4 BX = AX + BX

AX = 4 BX - BX

AX = 3BX

 

AX/BX = AY/YC

[corresponding sides of similar triangles are proportional]

3BX /BX = AY/2

3/1 = AY/2

AY = 3 × 2  

AY = 6 cm

Hence, the Length of AY is 6 cm.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

$\huge\bold\pink{Answer}$
Length of AY is 6 cm.

ꜱᴏʟᴜᴛɪᴏɴ----

=>xy ɪꜱ ᴩᴀʀᴀʟʟᴇʟ ᴛᴏ ʙᴀꜱᴇ.ꜱᴏ xy ᴄᴜᴛꜱ ʙᴏᴛʜ ᴀʙ ᴀɴᴅ ᴀᴄ ɪɴ ꜱᴀᴍᴇ ʀᴀᴛɪᴏ.

=>ɢɪᴠᴇɴ:ᴀʙ=4ʙx

ᴛʜᴇʀᴇꜰᴏʀᴇ,
ᴀx:ʙx=3:1

ꜱɪᴍɪʟᴀʀʟy,
ᴀy:ᴄy=3:1

ɢɪᴠᴇɴ:ᴄy=2 ᴄᴍꜱ

ꜱᴏ ᴀy=3×2
ᴀy=6 ᴄᴍꜱ