The area of a rectangle is 360 sq cms. which is equal to 90% of the area of a square. What is the side of the square?

Options

A. 20cms
B. 15cms
C. 40cms
D. 25cms.

Answer

To find the side of the square given that the area of a rectangle is 360 sq cms and is equal to 90% of the area of the square, we can follow these steps:

### Step 1: Understand the relationship between the areas
We know that the area of the rectangle (A_rectangle) is 360 sq cms, and this area is 90% of the area of the square (A_square).

### Step 2: Set up the equation
Let the side of the square be \( x \). Therefore, the area of the square can be expressed as:
\[ A_{square} = x^2 \]
According to the problem, we have:
\[ A_{rectangle} = 0.9 \times A_{square} \]
Substituting the known values:
\[ 360 = 0.9 \times x^2 \]

### Step 3: Solve for \( x^2 \)
To isolate \( x^2 \), divide both sides of the equation by 0.9:
\[ x^2 = \frac{360}{0.9} \]

### Step 4: Calculate \( x^2 \)
Calculating the right side:
\[ x^2 = 400 \]

### Step 5: Find \( x \)
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{400} \]
\[ x = 20 \]

### Conclusion
The side of the square is 20 cm.

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