XY is drawn parallel to the base BC of a - ABC cutting AB at X and AC at Y- If AB -4 BX and CY - 2 cm- then the value of AY is equal to -

The correct option is A 6 cm In AXY and ABC ∠ AXY= ∠ B [corresponding angle] ∠ A = ∠ A ∴ AXY ∼ ABC [AA Similarity]Given AB ...

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Byju's Answer

Standard VII

Mathematics

Construction of Triangles: When 2 Sides and Included Angle Are Given

XY is drawn p...

Question

$X Y$ is drawn parallel to the base $B C$ of a $Δ A B C$ cutting $A B$ at $X$ and $A C$ at $Y$ . If $A B = 4 B X$ and $C Y = 2 c m,$ then the value of $A Y$ is equal to :

2 c m

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4 c m

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6 c m

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8 c m

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Solution

The correct option is A $6 c m$
In $△ A X Y$ and $△ A B C$
$∠ A X Y = ∠ B$ [corresponding angle]
$∠ A = ∠ A$
$∴ △ A X Y \sim △ A B C$ [AA Similarity]
Given $A B = 4 B X$
Let $B X = x$
$∴ A B = 4 x$ i.e, $A X = 3 x$
$\frac{A X}{B X} = \frac{A Y}{Y C} \Rightarrow \frac{3 x}{x} = \frac{A Y}{2}$
$\Rightarrow A Y = 6 c m$

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Similar questions

Q. XY is drawn parallel to the base BC of a ∆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

$XY is drawn parallel to the base BC of a Δ A B C cutting AB at X and AC at Y. If AB = 4 cm, BX and YC = 2 cm,$
$then find the measure of AY .$

D E

is drawn parallel to the base

B C

of a

△ A B C

, meeting

A B

D

and

A C

E, \frac{A B}{A C} = 4

and

C E = 2 c m

, find

A E

In $Δ A B C, A B = B C = 6 c m$ . If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then $Δ A B C \sim Δ E B D$ .

Q. In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then

(a) BC = CY
(b) BC = BY
(c) BC ≠ CY
(d) BC ≠ BY

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XY is drawn parallel to the base BC of a ΔABC cutting AB at X and AC at Y. If AB=4BX and CY=2 cm, then the value of AY is equal to :

The correct option is A 6cmIn △AXY and △ABC∠AXY=∠B [corresponding angle]∠A=∠A∴△AXY∼△ABC [AA Similarity]Given AB=4BXLet BX=x∴AB=4x i.e, AX=3xAXBX=AYYC⇒3xx=AY2⇒AY=6cm

$X Y$ is drawn parallel to the base $B C$ of a $Δ A B C$ cutting $A B$ at $X$ and $A C$ at $Y$ . If $A B = 4 B X$ and $C Y = 2 c m,$ then the value of $A Y$ is equal to :