Find, area of \triangle A D E : area of quadrilateral BCED.

ICSE Class X Math 2015 Solved Paper - Question 49

$A B C$ is a right angled triangle with $∠ A B C=$ $90^{∘} . D$ is any point on $A B$ and $D E$ is perpendicular to AC. Prove that :

Question : 49 of 52

Marks: +1, -0

Find, area of

△ A D E

: area of quadrilateral BCED.

Solution:

\;\;{\;\text " Ar. of "\;(△ {\ABC})}/{\;\text " Ar. of "\;(△ {\ADE})}=\;{ {\AB}^2}/{ {\AE}^2}

=\;{144}/{16}=\;{9}/{1}

\;\;{\;\text " Ar. of "\;(△ {\ADE})+ {\Ar} \;\text ". of "\;( {\BCED})}/{ {\Ar} \;\text ". of "\;(△ {\ADE})}=9

\;1+\;{\;\text " Ar. of "\;(B C E D)}/{\;\text " Ar. of "\;(△ A D E)}=9

\;\;{\;\text " Ar. of "\;(△ {\ADE})}/{\;\text " Ar. of "\;( {\BCED})}=\;{1}/{8}

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