The Sarpanch of a village Padampur requested one of his villagers to donate a 6 m wide land
adjusted to his 132.8 m long side of his right triangular plot outside the village. The other sides of
the plot are 123 m and 50 m. On his donated land, the Sarpanch wants to construct a link road
which provides the connectivity with the other villages and towns. The villager agreed at once.
(i) Find the area of triangular plot remaining with the villager.
(ii) What are the values involved here?
Answers
Answer:
Step-by-step explanation:
Solution :-
In right ∆ABC,
→ tan θ = AB / BC
→ tan θ = 50/123
→ θ = tan^(-1)(50/123)
→ θ = 22.12°
so, in right ∆EFC,
→ tan θ = EF/FC
→ tan 22.12° = 6/FC
→ FC = 6 / 0.41
→ FC = 14.6 m .
then,
→ DE = AC - (AG + FC) = 132.8 - 2*14.6 = 132.8 - 29.2 = 103.6 m .
now, In right ∆DBE,
→ DB = sin θ * DE = 0.38 * 103.6 = 39.4 m .
→ BE = cos θ * DE = 0.93 * 103.6 = 96.3 m .
therefore,
→ Remaining Area = Area(∆ABC) - Area(DBE) = (1/2)[50*123 - 39.4*96.3] = (1/2)[6150 - 3794.22] = (1/2)(2355.78) = 1177.9 m² (Ans.)
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