Question

In the figure, DE || BC such that AD = 4.8
cm, AE = 6.4 cm and EC = 9.6 cm, find
AB
​

Answer 1

Answer:

12 cm

Step-by-step explanation:

AD/BD=AE/EC

(PROPORTIONALITY THEOREM)

4.8/BD=6.4/9.6

BD=4.8×9.6/6.4

BD=7.2

AB=4.8+7.2=12 cm

Answer 2

The value of AB = 12 cm.

Step-by-step explanation:

The basic proportionality theorem states that if in a triangle, there exists a line that intersects two sides of the triangle in two discrete points and the line is parallel in nature to the third side of the triangle, the line basically bisects the two sides of the triangle it intersects in two discrete points, then, the ratio of the bisected parts of each intersected side is equal to each other.

According to the given information, we have the length of AD of the triangle as 4.8 cm., the length of AE as 6.4 cm. and the length of EC as 9.6 cm. Also, we have the line DE parallel to the side BC of the triangle and it intersects the two sides AB and AC in two distinct points namely D and E.

Then, by the basic proportionality theorem, we have,

$\frac{AD}{DB}=\frac{AE}{EC}$

Now, putting the values of the sides, we get,

$\frac{4.8}{DB}=\frac{6.4}{9.6}$

Or, DB = $\frac{4.8*9.6}{6.4}$

or, DB = 7.2 cm.

Now, AB is equal to AD + DB.

Then, AB = 4.8 + 7.2 = 12 cm.

Thus, the value of AB = 12 cm.

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