In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)
To solve this question, we need to determine the length of RS in the parallelogram PQRS. Given are PS = 7 cm, PT = 4 cm, and PV = 5 cm.
First, observe that the given figure contains right triangles \(PTQ\) and \(PVR\):
- \(\triangle PTQ\) has PT = 4 cm and this triangle is a right triangle.
- \(\triangle PVR\) also forms a right triangle with PV = 5 cm.
Since PQRS is a parallelogram, opposite sides are equal, hence PQ = RS.
Using the Pythagorean theorem in the right triangle \(\triangle PVR\), we have:
\(PV^2 + VR^2 = PR^2\)
We know: \(PV = 5\) cm.
To find VR, observe that VR = QT:
\(QT = \frac{PS \times PT}{PV} = \frac{7 \times 4}{5} = \frac{28}{5} \text{ cm}\)
Since opposite sides in a parallelogram are equal:
\(RS = QT = \frac{28}{5} \text{ cm}\)
Thus, the length of RS is \(\frac{28}{5} \text{ cm}\), which matches the correct option.
| Option | Length |
|---|---|
| \(\frac{20}{7}\) | Doesn't satisfy |
| \(\frac{28}{5}\) | Correct, as computed |
| \(\frac{9}{2}\) | Doesn't satisfy |
| \(\frac{35}{4}\) | Doesn't satisfy |
Therefore, the correct answer is \(\frac{28}{5}\).
Important Questions from Mensuration and Geometry
In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in cm²) of the rectangle PLMN?
Note: The figure shown is representative.
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r$ cm as shown in the figure. The side of the dodecagon is $d$ cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side $r$ cm and each numbered triangle is used only once to form a square.
The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
Note: The figure shown is representative.
- Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?
- A circle with center at $(x, y) = (0.5, 0)$ and radius $= 0.5$ intersects with another circle with center at $(x, y) = (1, 1)$ and radius $= 1$ at two points. One of the points of intersection $(x, y)$ is:
- During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of the Earth-Sun and Earth-Moon distances is closest to
