In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.

Home » In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.

In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.

Answer:

Given,

DE || BC.

∠???????????? = ∠???????????? (???????????????????????????????????????????????????? ????????????????????????)

Applying AA similarity theorem,

∆ ADE ~ ∆ABC

$\frac{\operatorname{ar}(\triangle A B C)}{a r(\triangle A D E)}=\frac{B C^{2}}{D E^{2}}$

Subtracting 1 from both sides,

$\frac{\operatorname{ar}(\triangle A B C)}{ar(\triangle A D E)}-1=\frac{5^{2}}{3^{2}}-1$

$\frac{\operatorname{ar}(\triangle A B C)-\operatorname{ar}(\triangle A D E)}{a x(\triangle A D E)}=\frac{25-9}{9}$

$\frac{\operatorname{ar}(B C E D)}{\operatorname{ar}(\triangle A D E)}=\frac{16}{9}$

$[O R]$

$\frac{\operatorname{ar}(\triangle A D E)}{a r(B C E D)}=\frac{9}{16}$

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