Question

In the given figure, DE || BC, then the value of x is equal to​

Answer 1

Answer:

Using, Thales theorem,

x+2/7 =x/2x

=> x+2/7 = 1/2

=>2x+4 = 7

=>2x =3

=>x =3/2

=>x = 1.5.

Answer 2

Answer:

There are several ways to solve this figure... But I think this is an easy method:

AD=x+2; DB=7. Thus, AB=AD+DB=x+2+7=x+9.

Similarly, AC=AE+EC=x+2x=3x.

Now, DE║BC. Thus, using corresponding angles theorem:

∠ADE=∠ABC; ∠AED=∠ACB.

Thus, ΔABC≅ΔADE.

We now know that the ratio sides of the corresponding triangles of similar triangles are equal. Thus,

AD/AB=AE/AC

(x+2)/(x+9)=x/3x

3(x+2)=1(x+9)

3x+6=x+9

3x-x=9-6

2x=3

x=3/2

x=1.5cm.

HOPE THIS HELPS :D