Maths / Areas Of Parallelograms And Triangles / Area of Triangle

QUESTION

In $\Delta$ABC, if a point D divides BC in the ratio 2 : 3, show that ar($\dpi{120} \fn_jvn \large \Delta$ABD) : ar ($\dpi{120} \fn_jvn \large \Delta$ACD) = 2 : 3.

EXPLANATION
Explain TypeExplanation Content
Text

Draw the angle.

page no. 2

Ans. no. 9

$Construction :\: AE\: \perp BC\\\\ ar(\Delta ABD)=\frac{1}{2}\times BD\times AE\\\\ ar(\Delta ABD)=\frac{1}{2}\times CD \times AE\\\\ ar\frac{\Delta ABD }{ar(\Delta ACD )}=\frac{\frac{1}{2}\times BD\times AE}{\frac{1}{2}\times CD\times AE}\\\\\\ \frac{ar(\Delta ABD)}{ar(\Delta ACD)}=\frac{BD}{CD}=\frac{2}{3}$

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