The length & breadth of a rectangle is in ratio 9:7. If perimeter of rectangle is 128 cm and side of square is 6 cm less than length of rectangle, then find area of the square.

Correct Answer: 900 cm²

Step-by-Step Explanation:

Step 1: Understand the given ratios and values.
Let the length of the rectangle be $l$ and the breadth of the rectangle be $b$.
The ratio of length to breadth is given as 9:7. Therefore, we can express length and breadth in terms of a common variable $x$:

$l=9x$

$b=7x$

Step 2: Use the perimeter of the rectangle to find $x$.
The perimeter of a rectangle is calculated using the formula:

$\text{Perimeter}=2\times (l+b)$

We are given that the perimeter is 128 cm. Substituting the expressions for $l$ and $b$:

$128=2\times (9x+7x)$

$128=2\times 16x$

$128=32x$

$x=\frac{128}{32}=4$

Step 3: Calculate the length of the rectangle.
Now substitute $x=4$ back into the expression for length:

$l=9\times 4=36\text{ cm}$

Step 4: Determine the side of the square.
The problem states that the side of the square (let's call it $s$) is 6 cm less than the length of the rectangle:

$s=l-6$

$s=36-6=30\text{ cm}$

Step 5: Calculate the area of the square.
The formula for the area of a square is:

$\text{Area}=s^2$

$\text{Area}={30}^2=900{\text{ cm}}^2$

Thus, the area of the square is 900 cm².