Question

In the given figure ABC is a triangle If AD = 3.6 cm. AB = 10 cm. AE = 1.8cm
length of AC to make DE||BC is
A] 10 cm
B] 7.2 cm
C] 20 cm
D] 5 cm​

Answer 1

In the given figure ABC is a triangle. AD = 3.6 cm. AB = 10 cm. AE = 1.8cm. The length of AC to make DE||BC is

Consider the attached figure while going through the following steps:

Given,

AD = 3.6 cm

AB = 10 cm

AE = 1.8 cm

Thales theorem states that, "If a line is drawn parallel to one side of a triangle intersecting the remaining sides, then it divides the 2 sides in the same ratio."

Assuming DE||BC and using the Thales theorem, we have,

AD / BD = AE / CE

AD / (AB - AD) = AE / CE

3.6 / (10 - 3.6) = 1.8 / CE

3.6 / 6.4 = 1.8 / CE

1 /2 = 1.8 / CE

CE = 2 × 1.8 = 3.6 cm

Now consider,

AC = AE + CE

= 1.8 + 3.6

∴ AC =  5.4 cm

Answer 2

Answer:

d) 5cm

Step-by-step explanation:

AB=AD+DB

10=3.6+DB

10-3.6=DB

6.4=DB

According to Thales (bpt) theorem

AD/DB=AE/EC

3.6/6.4=1.8/EC(cross multiply)

11.52=3.6EC

11.52/3.6=EC

3.2=EC

AC =AE/EC

1.8+3.2

5.0

that is nothing but 5