The class IX students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity . Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other . There is a lawn PQRS in the ground as shown in the below figure:
1. What are the coordinates of C, taking A as origin?
C (6,10)
C (10,10)
C (6,6)
C (10,6)
B)Shape of lawn is
Square
Rectangle
Parallelogram
Rhombus
C)Area of lawn is:
30 sq units
60 sq units
45 sq units
None of the above
Answers
Answer:
1. (10,6)
2. Rhombus
3. 30 sq. units
Solution :-
a)
→ The coordinates of C, taking A as origin = (10, 6)
b)
→ Coordinates of P = (5,0)
→ Coordinates of Q = (10,3)
→ Coordinates of R = (5,6)
→ Coordinates of S = (0,3)
So,
→ PQ = √[(10 - 5)² + (3 - 0)²] = √[5² + 3²] = √(25 + 9) = √34 units
→ RS = √[(5 - 0)² + (6 - 3)²] = √[5² + 3²] = √(25 + 9) = √34 units
→ QR = √[(10 - 5)² + (3 - 6)²] = √[5² + (-3)²] = √(25 + 9) = √34 units
→ PS = √[(5 - 0)² + (0 - 3)²] = √[5² + (-3)²] = √(25 + 9) = √34 units
and,
→ PR = √[(5 - 5)² + (6 - 0)²] = √[0 + 6²] = √(36) = 6 units
→ QS = √[(10 - 0)² + (3 - 3)²] = √[10² + 0] = √(100) = 10 units
as we can see that, all sides are equal but diagonals are not equal .
therefore, Shape of lawn is Rhombus .
c)
→ Area of lawn = (1/2) * PR * QS = (1/2) * 10 * 6 = 30 units²
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