Question

In Fig. 4.178,DE||BC
(i) If DE = 4 cm, BC = 6 cm and area (ΔADE) = 16 cm², find the area of ΔABC.
(ii) If DE = 4 cm, BC = 8 cm and area (ΔADE) = 25 cm², find the area of ΔABC.
(iii) If DE : BC = 3 : 5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.

Answer 1

Answer:

In △ABC AB=AC

⇒∠B=∠C (Angles opposite to equal sides are equal)

Now using angle sum property

∠A+∠B+∠C=180

∘

⇒80

∘

+∠C+∠C=180

∘

⇒2∠C=180

∘

−80

∘

⇒∠C=

2

100

∘

​

=50

∘

now ∠C+∠x=180

∘

(Angles made on straight line (AC) are supplementary)

⇒50

∘

+∠x=180

∘

⇒∠x=180

∘

−50

∘

=130

∘

@ARSH

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Step-by-step explanation: