Question

The ratio between length and breadth of a rectangle is \(3:2\). If area of the rectangle is \( 96cm^2\), then length of the rectangle is

• A. 6 cm
• B. 12 cm
• C. 8 cm
• D. 16 cm

Answer 1

The Correct Option is B

The problem involves finding the length of a rectangle given its area and the ratio between its length and breadth. Let's denote the length of the rectangle as 3x and its breadth as 2x, based on the given ratio \(3:2\).

The area of a rectangle is calculated as:

$\mathrm{Area}=\mathrm{length}\times \mathrm{breadth}$

Therefore, we have:

$96=3x\times 2x$

Solving for x:

$96=6x^2$

We then divide both sides by 6:

$x^2=16$

Taking the square root of both sides gives us:

$x=4$

Thus, the length of the rectangle, which is 3x, is:

$3\times 4=12$

Therefore, the length of the rectangle is 12 cm.