Question

Tell me If you now dude ​

Answer 1

Answer:

c)

Step-by-step explanation:

Area of Triangle ABC = 1/2 × BC × AD

Area of Triangle ABC by Heron's formula -

$\sqrt{ \frac{5a}{2} ( \frac{5a}{2} - 2a)( \frac{5a}{2} - 2a)( \frac{5a}{2} - a) }$

Now as both are to find the area, we can equate them, so -

$\frac{1}{2} \times a \times x = \sqrt{ \frac{15 {a}^{4} }{16} } \\ = > ( { \frac{ax}{2} })^{2} = \frac{15 {a}^{4} }{16} \\ = > \frac{ {x}^{2} }{4} = \frac{15 {a}^{2} }{16} \\ = > 4 {x}^{2} = 15 {a}^{2} \\ = > x = \frac{a}{2} \sqrt{ {15} }$

Where x = AD

Hence AD = a/2 × √15