Question

Quadrilaterals
353
C
36. In a trapezium ABCD, if AB || CD then (ACP + BD3) = ?
(a) BC? + ADP + 2BC · AD
(b) AB? + CD² + 2ABCD
(C) AB+ CD + 2AD. BC
(d) BC? + ADP + 2AB. CD
A
B​

Answer 1

Step-by-step explanation:

$a {c}^{2} + b {d}^{2} \\ = (a {l}^{2} + l {c}^{2} ) + (b {m}^{2} + m {d}^{2} ) \\ = (am + ml)^{2} + l {m}^{2} + (b {l}^{2} + l {c}^{2} ) + m {d}^{2} \\ = (a {m}^{2} + m {d}^{2} ) + (b {l}^{2} + l {c}^{2} ) + 2m {l}^{2} + 2am \times \: ml + 2bm \times ml \\ = a {d}^{2} + b {c}^{2} + 2ml(ml + am + bl) \\ a {d}^{2} + b {c}^{2} + 2cd \times ab (ml = cd$