Calculating the Area of a Rectangle Using Its Perimeter

In this article, we will explore the relationship between the perimeter and the area of a rectangle, specifically using the given values and solving for the area. We will go through multiple examples to understand how to derive the dimensions of the rectangle and calculate its area.

Example 1

The perimeter of a rectangle is 79 metres. The ratio of length and breadth is 4:4. What is the area of the rectangle?

Given:

Perimeter (P) 79 metres Ratio of length (L) to breadth (B) 4:4

Since the ratio is 4:4, the rectangle is actually a square. Therefore, L B.

Let L B. Perimeter of a rectangle 2(L B) 2(L L) 2 × 2L 4L 79 metres. Solving for L: 4L 79 L 79 / 4 19.75 metres B L 19.75 metres

The area (A) of the rectangle is given by:

A  L × B  19.75 × 19.75  390.0625 square metres

Example 2

Given the perimeter is 79 metres and the length to breadth ratio is 3:4, we need to find the area.

Let:

Length (L) f Breadth (B) 0.6f

The perimeter (P) 2(L B) 2(f 0.6f) 2.2f 79 metres.

Solving for f: 2.2f 79 f 79 / 2.2 35.91 metres B 0.6f 0.6 × 35.91 21.55 metres

The area (A) of the rectangle is given by:

A  L × B  35.91 × 21.55  776.7045 square metres

Example 3

Given the perimeter (P) 60 metres, the length (L) n, and the breadth (B) 3n/7, we need to find the area.

The perimeter (P) 2(L B) 2(n 3n/7) 20n/7 60 metres.

Solving for n: 20n/7 60 n (60 × 7) / 20 21 metres B 3n/7 3 × 21 / 7 9 metres

The area (A) of the rectangle is given by:

A  L × B  21 × 9  189 square metres

Example 4

Given the perimeter of a rectangle is 79 metres, the length to breadth ratio is L:B 3:4, we need to find the area.

The perimeter (P) 2(L B) 2(39.5 - 34.5) 79 metres, where 39.5 is the total length and 34.5 is the remaining length.

Solving for L and B: L 17 metres B 22.5 metres

The area (A) of the rectangle is given by:

A  L × B  17 × 22.5  382.5 square metres

Example 5

Given the perimeter (P) 79 metres, the length (L) to breadth (B) ratio is 4:4, the rectangle is actually a square. The sides are 19.75 metres, and the area (A) is:

A  19.75 × 19.75  390.0625 square metres

Example 6

Given the perimeter (P) 39.5 metres, the length (L) to breadth (B) ratio is 49:34, we solve for L and B:

Let:

Perimeter (P) 39.5 metres Ratio of L to B 49:34 B 49L/34

Perimeter (P) 2(L B) 2(L 49L/34) 79L/17 39.5 metres.

Solving for L: 79L/17 39.5 L (39.5 × 17) / 79 7.4 metres B 49 × 7.4 / 34 10.8 metres

The area (A) of the rectangle is given by:

A  L × B  7.4 × 10.8  79.92 square metres

In conclusion, by applying the formula for the perimeter and area of a rectangle, we can accurately determine the dimensions and area of a rectangle given its perimeter and ratio of length to breadth.