Question

If the area of a rectangle is \(112\ m^2\) and its length is \(6\ m\) more than the breadth, then the breadth of the rectangle is

• A. 8 m
• B. 14 m
• C. 10 m
• D. 12 m

Answer 1

The Correct Option is A

1. Let the breadth of the rectangle be \( x \) meters:

Since the length is 6 meters more than the breadth, the length is \( x + 6 \) meters.

2. Using the formula for the area of a rectangle:

The area is given by: \( \text{Area} = \text{Length} \times \text{Breadth} \).

We know the area is 112 m², so:

\( x(x + 6) = 112 \)

3. Simplifying the equation:

Expand the equation: \( x^2 + 6x = 112 \)

Rearrange it to form a quadratic equation:

\( x^2 + 6x - 112 = 0 \)

4. Solving the quadratic equation:

We can solve it using the quadratic formula:

\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Here, \( a = 1 \), \( b = 6 \), and \( c = -112 \).

Substitute these values into the quadratic formula:

\( x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-112)}}{2(1)} \)

\( x = \frac{-6 \pm \sqrt{36 + 448}}{2} \)

\( x = \frac{-6 \pm \sqrt{484}}{2} \)

\( x = \frac{-6 \pm 22}{2} \)

Therefore, \( x = \frac{-6 + 22}{2} = \frac{16}{2} = 8 \) or \( x = \frac{-6 - 22}{2} = \frac{-28}{2} = -14 \).

Since the breadth cannot be negative, we have \( x = 8 \) meters.