Rectangular Park Perimeter Calculation
We are given a rectangular park with the following information:
- Diagonal length, d = 25 meters
- Length of one side, l = 15 meters
We need to find the perimeter of the park.
Finding the Other Side Length
In a rectangle, the diagonal, length, and width form a right-angled triangle. We can use the Pythagorean theorem: $l^2 + w^2 = d^2$, where w is the width (the other side).
- Substitute the known values: ${15}^2 + w^2 = {25}^2$.
- Calculate the squares: $225 + w^2 = 625$.
- Isolate $w^2$: $w^2 = 625 - 225$.
- Calculate $w^2$: $w^2 = 400$.
- Find the width w by taking the square root: $w = \sqrt{400}$.
- Result: $w = 20$ meters.
Calculating the Perimeter
The perimeter of a rectangle is calculated using the formula: Perimeter = $2 \times (length + width)$.
- Substitute the side lengths we found: Perimeter = $2 \times (15 + 20)$.
- Add the lengths: Perimeter = $2 \times (35)$.
- Calculate the final perimeter: Perimeter = 70 meters.
Therefore, the perimeter of the rectangular park is 70 meters.
Important Questions from Mensuration 2D (Notes)
- Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use $\sqrt{7} = 2.6$).
- Find the area of a regular hexagon whose side measures $14\sqrt{3}$ cm.
- Find the perimeter of the semi-circle of radius 21 cm.
$\left(\text{Take } \pi = \frac{22}{7}\right)$ - If the area of an equilateral triangle is given as $900 \text{ m}^2$, then what is its perimeter?
The difference between two parallel sides of a trapezium is 9 cm. The perpendicular distance between them is 52 cm. If the area of the trapezium is 988 \(cm^2\), find the lengths of the parallel sides (in cm).
