D
8. In the given figure, ABC is an
equilateral triangle. DE is parallel
to BC such that area of quadrilateral
DBCE is equal to one half the area
of AABC. If BC = 2 cm, then DE
Answers
Given : ABC is an equilateral triangle.
DE is parallel to BC such that area of quadrilateral DBCE is equal to one half the area of ΔABC. BC = 2 cm,
To Find : DE
Solution:
area of ΔABC = area of quadrilateral DBCE + area of ΔADE
area of quadrilateral DBCE is equal to one half the area of ΔABC
=> area of ΔABC = (1/2) area of ΔABC + area of ΔADE
=> area of ΔADE = (1/2) area of ΔABC
DE || BC
=> ∠D = ∠B and ∠E = ∠C corresponding angles
=> ΔADE ~ ΔABC Using AA similarity
=> Area of ΔADE / Area of ΔABC = (DE/BC)²
=> 1/2 = (DE/2)²
=> DE² = 2
=> DE = √2
Hence DE is √2
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