Question

Please help me guys by solving this questions step by step​

Answer 1

Answer:

Option (3) is the correct answer!

Step-by-step explanation:

From the figure description, let me take as:

<1 = <2 = <3 and;

Perimeter of triangle BEC = 13cm;

With this conclusion the solution is given as below.

Let <1 = <2 = <3 = u and <ABD = v

=> <ABC = u + v and <BDC = u + v

Also <DEC = 2u

Applying law of sines to triangle BCD,

BC/sin(u + v) = DC/sin(u)

=> BC/sin(u + v) = 4/sin(u) ---------- (1)

iv) Again applying sine law to triangle ABC,

AC/sin(u + v) = BC/sin(u)

=> 9/sin(u + v) = BC/sin(u) ------- (2)

Dividing (1) by (2):

BC/9 = 4/BC

=>BC^2 = 36

So, BC = 6 cm

As perimeter of triangle BEC = 13,

=> BE + EC + BC = 13

=> 2BE = 13 - BC = 7 cm [As <1 = <2, BE = CE]

So BE = 3.5 cm

Thus,

BE = 3.5cm

Hope it helps!

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