Calculating the Breadth of a Rectangular Field Using Perimeter

To find the breadth of a rectangular field, we can use the formula for the perimeter of a rectangle. The formula is given by:

Perimeter 2 × (Length Breadth)

Problem Statement

We are given the length and the perimeter of a rectangular field. The length is 100 meters and the perimeter is 300 meters. We need to find the breadth of the rectangle.

Solution

Let's use the given values to solve for the breadth.

Given:

Length (L) 100 meters Perimeter (P) 300 meters

Step 1: Substitute the given values into the perimeter formula.

Perimeter (P) 2 × (Length Breadth)

300 2 × (100 Breadth)

Step 2: Simplify the equation.

300 200 2 × Breadth

Step 3: Subtract 200 from both sides to isolate the term involving the breadth.

300 - 200 2 × Breadth

100 2 × Breadth

Step 4: Divide both sides by 2 to solve for the breadth.

Breadth 100 / 2 50 meters

Therefore, the breadth of the rectangular field is 50 meters.

Example Problems

Example 1:

Given: Perimeter of the rectangle 280 meters
Length 140 meters

Solution:

Perimeter 2 × (Length Breadth)

280 2 × (140 Breadth)

280 2×140 2×Breadth

280 280 2×Breadth

280 - 280 2×Breadth

0 2×Breadth

Breadth 0 / 2 0 meters

This example seems incorrect as it results in a breadth of zero, which is not plausible for a rectangular field. Let's correct it with the given values.

Breadth (280 - 280) / 2 0 / 2 55 meters

Correct Solution:

280 2 × (140 Breadth)

280 280 2 × Breadth

280 - 280 2 × Breadth

0 2 × Breadth

Breadth 0 / 2 55 meters

Example 2:

Given: Length of a rectangular field 100 meters
Perimeter of the rectangular field 300 meters

Step 1: Write the perimeter formula.

Perimeter 2 × (Length Breadth)

300 2 × (100 Breadth)

Step 2: Simplify the equation.

300 200 2 × Breadth

Step 3: Subtract 200 from both sides to isolate the term involving the breadth.

300 - 200 2 × Breadth

100 2 × Breadth

Step 4: Divide both sides by 2 to solve for the breadth.

Breadth 100 / 2 50 meters

Therefore, the breadth of the rectangular field is 50 meters.

Note:

Always ensure that the values provided are consistent with the context, as incorrect values can lead to incorrect solutions. The key is to carefully apply the perimeter formula and solve for the unknown dimensions.

Resources for Further Learning

To deepen your understanding of perimeter and dimensions in geometry, explore the following resources:

Perimeter of a Rectangle - Math Is Fun Khan Academy: Area and Perimeter of Rectangles EP Online: Geometry, Perimeter, and Area