If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm…
2023
If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively. Calculate the area of the rectangular field.
- A.
25 cm^2
- B.
20 cm^2
- C.
29 cm^2
- D.
18 cm^2
Attempted by 10 students.
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Correct answer: B
Solution: Let the length be l and the width be w.
Perimeter: 2(l + w) = 18, so l + w = 9.
Diagonal: (√41)^2 = l^2 + w^2, so l^2 + w^2 = 41.
Use identity (l + w)^2 = l^2 + w^2 + 2lw. Substitute known values: 9^2 = 41 + 2lw, so 81 = 41 + 2lw.
Solve for area: 2lw = 81 - 41 = 40, hence lw = 20. The area is 20 cm^2.
Answer: 20 cm^2