Length of rectangle 'A' is 125% of its breadth and area of rectangle 'A' is `1280 cm^(2).` If width of rectangle 'A' is half of the side of a square, then find side of square.

Options

A. A)72m
B. B)64m
C. C)84m
D. D)96m

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let the breadth (width) of rectangle A be \( b \) cm. According to the problem, the length \( l \) of rectangle A is 125% of its breadth. This can be expressed as:
\[ l = 1.25b = \frac{5}{4}b \]

### Step 2: Write the Area Formula
The area \( A \) of rectangle A is given by the formula:
\[ A = l \times b \]
We know from the problem that the area is \( 1280 \, \text{cm}^2 \). Substituting the expression for length, we have:
\[ A = \left(\frac{5}{4}b\right) \times b = \frac{5}{4}b^2 \]

### Step 3: Set Up the Equation
Setting the area equal to \( 1280 \, \text{cm}^2 \):
\[ \frac{5}{4}b^2 = 1280 \]

### Step 4: Solve for \( b^2 \)
To eliminate the fraction, multiply both sides by 4:
\[ 5b^2 = 1280 \times 4 \]
Calculating the right side:
\[ 5b^2 = 5120 \]
Now, divide both sides by 5:
\[ b^2 = \frac{5120}{5} = 1024 \]

### Step 5: Find \( b \)
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{1024} = 32 \, \text{cm} \]

### Step 6: Find the Side of the Square
According to the problem, the width of rectangle A is half of the side of a square. Therefore, if \( s \) is the side of the square:
\[ b = \frac{s}{2} \]
Substituting \( b = 32 \, \text{cm} \):
\[ 32 = \frac{s}{2} \]
Multiplying both sides by 2:
\[ s = 64 \, \text{cm} \]

### Final Answer
The side of the square is \( 64 \, \text{cm} \).

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