Question

In the figure, DE || BC.
DE = 4 cm, BC = 8 cm,
A(A ADE) = 25 cm? find A(A ABC)​

Answer 1

Step-by-step explanation:

☘$Answer:-$

$\: \: \:$

✪$Given:-$

$DE \: ∥ \: BC$

$In \: \: ΔADE \: \: and \: \: ΔABC$

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✪$To \: \: find:-$

$the \: \: area \: \: of \: \: ΔABC.$

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✪$Solution:-$

$We \: \: know \: \: that,$

$∠ADE \: = \: ∠B \:  [Corresponding \: \: angles]$

$∠DAE \: = \: ∠BAC \:  [Common]$

$Hence, \: \: ΔADE \: ~ \: ΔABC \: (AA \: \: Similarity)$

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$Since \: \: the \: \: ratio \: \: of \: \: areas \: \: of \\ two \: \: similar \: \: triangles \: \: is \: \: equal \\ to \: \: the \: \: ratio \: \: of \: squares \: \: of \: \: their \\ corresponding \: \: sides, \: \: we \: \: have,$

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⇨ $\frac{AR\: \: ΔADE\: }{AR \: ΔABC} = \: \frac{DE²}{BC²}$

⇨ $\frac{25 \: }{AR \:Δ ABC \: } \: = \frac{4²}{8²}$

⇨ $AR \: (ΔABC) \: = \: ( \frac{8 {}^{2} \times 25 }{4 {}^{2} } )$

⇨ $AR\:Δ ABC \: = \: 100cm {}^{2}$

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$Hence, \: \: the \: \: area \: \: of \: \: ΔABC \: \: is \: \: 100 cm {}^{2}$

Answer 2

Step-by-step explanation:

Science is the pursuit and application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence. Scientific methodology includes the following: ... Evidence. Experiment and/or observation as benchmarks for testing hypotheses.