Question
The length of a diagonal of a rectangular park is 25 meters, and that of one of its sides is 15 meters. Find the perimeter of the park.
The correct answer is
70 meters
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.
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Important Questions from Mensuration 2D (Notes)
- $P_1$ and $P_2$ are two regular polygons. The sum of all the interior angles of $P_1$ is $1800^\circ$. Each interior angle of $P_2$ exceeds its exterior angle by $120^\circ$. The difference between the number of sides of $P_1$ and $P_2$ is:
- The perimeter of the triangle is 24 cm and if the sides of the triangles are by prime numbers then the half of the area of triangle (in $cm^2$) is:
- The area of a square is 324 cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
- If the area of a rhombus is $10 \text{ cm}^2$ and one of its interior angles is $150^\circ$, what is the perimeter (in cm) of the rhombus?
- If the area of a rhombus is 10 cm$^2$ and one of its interior angles is 150°, what is the perimeter (in cm) of the rhombus?
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