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Question Number 106123 by DeepakMahato last updated on 03/Aug/20

I n a △ A B C w i t h s i d e s a = 6 c m, b = ? a n d c = ?

a r e a i s 270 {c m}^{2} . A n d i f

m i d l i n e o f t h e △ i s 7 c m

f i n d t h e v a l u e o f s i d e s b a n d c .

P l e a s e s o l v e t h i s w i t h a l i t t l e

e x p l a n a t i o n .

Commented by PRITHWISH SEN 2 last updated on 03/Aug/20

∵ a = 6 cm and the midline is 7 cm

∴ the midline must be parallal to b or c

∴ b or c = 14 cm and you may consider any of the

b or c side It {does}^{'} nt affect the overall calculation .

Commented by 1549442205PVT last updated on 03/Aug/20

Question lead to a cotradiction thing

Indeed, the midpoint l must be / / b or

/ / c and then b = 2 \times 7 = 14 cm or

c = 2 \times 7 cm = 14 cm

i) If l / / b then b = 14 cm and S_{Δ ABC} = \frac{1}{2} absinC

= \frac{7 \times 6 \times sinC}{2} = 21 sinC ⩽ 21 << 270 ({cm}^{2})

ii) If l / / c thi c = 2 l = 14 (cm)

\Rightarrow S_{Δ ABC} = \frac{acsinB}{2} = 21 sinB ⩽ 21 << 270

In other words, there {isn}^{'} t exist

any triangle that satisfying the

conditions of given problem!