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Relation between Areas and Sides of Similar Triangles

In the given ...

Question

In the given figure, BC is parallel to DE. Area of triangle ABC = 25 $c m^{2}$ , Area trapezium BCED = 24 $c m^{2}$ and DE = 14 cm. Calculate the length of BC. Also, find the area of triangle BCD.

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Solution

In ΔABC and Δ ADE,

As BC ∥ DE, corresponding angles are equal

∠ABC = ∠ADE

∠ACB = ∠AED

ΔABC ~ ΔADE

$fraction numerator a r open parentheses increment A B C close parentheses over denominator a r open parentheses increment A D E close parentheses end fraction equals fraction numerator B C squared over denominator D E squared end fraction 25 over 49 equals fraction numerator B C squared over denominator 14 squared end fraction open parentheses a r open parentheses increment A D E close parentheses equals a r open parentheses increment A B C close parentheses plus a r open parentheses t r a p e z i u m space B C E D close parentheses close parentheses B C squared equals 100 B C equals 10 i n space t r a p e z i u m space B C E D a r e a equals 1 half open parentheses s u m space o f space p a r e l l e l space s i d e s close parentheses cross times h g i v e n colon a r e a space o f space t r a p e z i u m space B C E D equals 24 space c m squared equals comma B C equals 10 c m space comma D E equals 14 space c m i e space 24 equals 1 half open parentheses 10 plus 14 close parentheses cross times h h equals fraction numerator 48 over denominator 10 plus 14 end fraction h equals 48 over 24 h equals 2 a r e a space o f space increment B C D equals 1 half cross times b a s e cross times space h e i g h t equals 1 half cross times B C cross times h equals 1 half cross times 10 cross times 2 equals 10 space c m squared$

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Similar questions

To the given figure, BC is parallel to DE Area of triangle $A B C = 25 c m^{2},$

Area of trapezium BCED $= 24 c m^{2}$ and DE =14 cm.

The length of BC = ___ cm.

B C ∥ D E

(△ A B C) = 25 {c m}^{2}

B C E D) = 24 {c m}^{2}

D E = 14 c m

B C

D E ∥ B C

△

c m^{2}

△

△

c m^{2}

△

△

In the figure BC || DE, area of ΔABC = 25 sq. cm, area of trapezium BCED = 24 sq. cm and DE = 14 cm. Calculate the length of BC.

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