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If D and E are the mid-points of the side AB and AC respectively of the ∆ ABC in the figure given here, the shaded region of the triangle is what per cent of the whole triangular region?
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- 50%
- 25%
- 75%
- 60%
- 50%
Correct Option: C
D is the mid-point of AB and E is the mid-point of AC.
∴ DE is parallel to BC.
and DE = 1 BC 2
∆ ADE and ∆ ABC are similar, because
D! = B! and E! = C!∴ ∆ ADE = DE² = 1 ∆ ABC BC² 4
⇒ 4∆ ADE = ∆ ABC
∴ Area of trapezium DBCE
= ∆ ABC – ∆ ADE
4∆ADE – ∆ADE = 3.∆ ADE∴ Required percentage = 3 × 100 = 75% 4
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