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(Chapter - Similarity)
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Answer:
Length of DE is equal to 10 cm.
Step-by-step explanation:
Given that DE || BC
this implies,
angle ADE = angle ABC ---------------(1)
angle AED = angle ACB ---------------(2)
{Reason: corresponding angles}
From (1)and (2) we can conclude that
∆ADE ~ ∆ABC
Area of ∆ADE = 25cm^2
Area of ∆ABC = (25+24) = 49cm^2
We know that 'The ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.'
=>area of ∆ADE/area of ∆ABC = DE^2/BC^2
=>√【area of ∆ADE/area of ∆ABC】= DE/BC
=>√【25/49】= DE/14
=>5/7 = DE/14
=>DE = (5×14)/7
=>DE = 10 cm
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