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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is a
  • a)
    Rectangle with one side 4cm
  • b)
    Parallelogram with one side 4cm
  • c)
    Square with one side 4 cm
  • d)
    Rhombus with each side 4cm
Correct answer is option 'D'. Can you explain this answer?
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Diagonal of Rectangle
The diagonal of a rectangle divides it into two congruent right triangles. Given that the length of the diagonal of Rectangle ABCD is 8 cm, we can use the Pythagorean theorem to find the length of the sides.

Midpoints of the sides
P, Q, R, and S are the midpoints of the sides AB, BC, CD, and DA respectively. Since P, Q, R, and S are the midpoints, they divide the sides of the rectangle into two equal parts.

Properties of Quadrilateral PQRS
- Since P, Q, R, and S are midpoints of the sides of the rectangle, PQRS is a parallelogram.
- In a parallelogram, the diagonals bisect each other. So, the length of the diagonal PR (which is also the diagonal of the rectangle) is 8 cm, which implies that PS = QR = 4 cm.

Conclusion
Since all the sides of quadrilateral PQRS are congruent (PS = QR = 4 cm), and the opposite angles are equal, we can conclude that the quadrilateral PQRS is a rhombus with each side measuring 4 cm. Therefore, the correct answer is option 'D' - Rhombus with each side 4 cm.
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer?
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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is aa)Rectangle with one side 4cmb)Parallelogram with one side 4cmc)Square with one side 4 cmd)Rhombus with each side 4cmCorrect answer is option 'D'. Can you explain this answer?.
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