Certainly! Let's walk through the problem step-by-step to find the length and breadth of the rectangle.
### Step 1: Understand the problem
We are given:
1. The ratio of the length to the breadth of the rectangle is [tex]\( \frac{5}{4} \)[/tex].
2. The area of the rectangle is [tex]\( 15180 \)[/tex] square centimeters.
### Step 2: Set up the formula
The area [tex]\( A \)[/tex] of a rectangle is given by the formula:
[tex]\[ A = \text{length} \times \text{breadth} \][/tex]
### Step 3: Define variables according to the ratio
Let the length [tex]\( \ell \)[/tex] be [tex]\( 5x \)[/tex] and the breadth [tex]\( b \)[/tex] be [tex]\( 4x \)[/tex], where [tex]\( x \)[/tex] is a common multiplier.
### Step 4: Express the area in terms of [tex]\( x \)[/tex]
From Step 3, we know:
[tex]\[ A = \ell \times b = (5x) \times (4x) = 20x^2 \][/tex]
Since the area is given as [tex]\( 15180 \)[/tex] square centimeters, we have:
[tex]\[ 20x^2 = 15180 \][/tex]
### Step 5: Solve for [tex]\( x \)[/tex]
To find [tex]\( x \)[/tex], we solve the equation:
[tex]\[ x^2 = \frac{15180}{20} = 759 \][/tex]
[tex]\[ x = \sqrt{759} \approx 27.54995462791182 \][/tex]
### Step 6: Calculate the length and breadth
Using [tex]\( x \)[/tex], we can now calculate the actual length and breadth.
1. Length:
[tex]\[ \ell = 5x = 5 \times 27.54995462791182 \approx 137.75 \text{ cm} \][/tex]
2. Breadth:
[tex]\[ b = 4x = 4 \times 27.54995462791182 \approx 110.20 \text{ cm} \][/tex]
### Final Answer
The length of the rectangle is approximately [tex]\( 137.75 \)[/tex] cm, and the breadth is approximately [tex]\( 110.20 \)[/tex] cm.
So, the length and the breadth of the rectangle are:
- Length: [tex]\( 137.75 \)[/tex] cm
- Breadth: [tex]\( 110.20 \)[/tex] cm
This completes our step-by-step solution!
