Answer:
To construct a parallelogram PQRS, follow these steps:
1. Draw a line segment PQ with a length of 5.8 cm.
2. From point P, draw a ray at an angle of 65°. This ray represents the side PS.
3. Measure 4.2 cm along this ray from point P and mark the endpoint as S.
4. Draw a line segment SR parallel to PQ and passing through point S.
5. Draw a line segment PR connecting points P and R.
6. Draw a line segment QS parallel to PR and passing through point S.
Now, to find the lengths of the diagonals PR and QS, you can use the properties of a parallelogram.
1. Diagonal PR:
- Since PQRS is a parallelogram, opposite sides are equal in length.
- Therefore, PR = PQ = 5.8 cm.
2. Diagonal QS:
- In a parallelogram, opposite angles are equal.
- Since angle PSR is 65°, angle PQR (opposite angle) is also 65°.
- Using the Law of Cosines, you can find the length of QS:
QS^2 = PQ^2 + PS^2 - 2 * PQ * PS * cos(PQR)
QS^2 = 5.8^2 + 4.2^2 - 2 * 5.8 * 4.2 * cos(65°)
QS ≈ 8.36 cm
So, the lengths of the diagonals PR and QS are approximately 5.8 cm and 8.36 cm, respectively
Explanation:
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