Question

In the figure ∆ ABC , DE || BC , AD = 1.5cm , DB = 6cm ,EC =8cm, AE =x find x = in following options a. 2.5 cm , b. 2cm ,c. 3cm, d. 3.5 cm
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Answer 1

Answer:

here we simply use BPT theorem

According to the given triangle

DE || BC

By using BPT theorem

AD/DB=AE/EC

Putting values

AD=1.5cm , DB=6cm , EC =8cm and AE =x cm

1.5/6=x/8

by cross multiplication

1.5×8/6=x

12/6=x

x=2cm

Thus, option (b) 2cm is correct

Answer 2

Question

In the figure ∆ ABC , DE || BC , AD = 1.5cm , DB = 6cm ,EC =8cm, AE =x find x = in following options a. 2.5 cm , b. 2cm ,c. 3cm, d. 3.5 cm

$\huge{ \underline{ \underline{ \bold{required \: answer}}}}$

●Basic Information ⬇️

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

●Given

It is given that AD=6 cm, DB=9 cm and AE=8 cm.

$\huge{ \underline{ \underline{ \bold{required \: Solution}}}}$

●Using the basic proportionality theorem, we have

AB/AD =AC/AE = BC/DE

⇒ AB/AD = AC/AE

_________________________

★ 15/6 = AC/8

⇒6AC=15×8

6/AC=120

⇒AC= 6/120 =20

__________________________

●hence, AC=20 cm.