Question

in the figure bc=10cm,bd=7cm,find dc​

Answer 1

$\Huge\boxed{\tt\green{✠Answer}}$

$\large \boxed{ \tt \red{Given:-}}$

$\sf \pink{BC=10 cm , BD=7 cm \: Area \: of \: ∆ABC \: in \: 50 \: sq.cm }$

$\large \boxed{ \tt \red{To \: Find : - }}$

$\sf \pink{ the \: area \: of \: ∆ABD \: and \: ∆ADC}$

✠Solution:-

$\sf{Draw \:  AE⊥ BC , BD  , CD }$

$\boxed{ \sf{Area \: of \: Triangle = \tt \frac{1}{2} \times Base \times height}}$

$\sf{Area \: of \:  ∆ABC =   \tt{ \frac{1}{2} \times BC \times AE   = 50}}$

$\sf \longrightarrow{  Area \: of  ∆ABC =   \tt \frac{1}{2} \times 10 \times AE   = 50}$

$\tt \longrightarrow{ \tt\frac{1}{2} \times AE  = 5}$

$\boxed{ \sf{Area \: of \: Δ ABD   = \tt \frac{1}{2}  BD \times AE}}$

$\sf \purple{ \longrightarrow 5 \times BD}$

$\sf \purple{ \longrightarrow 5 \times 7 }$

$\boxed{ \tt{ 35 cm²}}$

$\sf{CD = BC - BD = 10 - 7 = 3 cm }$

$\sf{Area \: of \: Δ ACD   = \tt \frac{1}{2} CD \times AE}$

$\sf \orange{ \longrightarrow5 \times CD}$

$\sf \orange{ \longrightarrow5 \times 3}$

$\boxed{ \tt{15 cm²}}$

$\bf \purple{ }$

$\bf \purple{}$

$\purple{\begin{cases} \bf Area \: of \: Δ ABD   = 35 cm² \\  \\  \bf Area \: of \: ΔACD   = 15 cm²\end{cases}}$