The length of a rectangular ground is 21 m more than its breadth. Its area is 31,042 m². Its breadth (in m) is:

The correct option is 161.

Step-by-step Explanation:

Let the breadth of the rectangular ground be $b$ meters.

According to the problem, the length ($l$) of the ground is 21 m more than its breadth:

$l=b+21$

The formula for the area of a rectangle is:

$\text{Area}=\text{Length}\times \text{Breadth}$

We are given that the area is 31,042 m². Substituting the expressions for length and area into the formula:

$(b+21)\times b=31042$

Expanding the left side gives a quadratic equation:

$b^2+21b-31042=0$

To solve this quadratic equation, we can factorize it by finding two numbers that multiply to -31,042 and add up to 21.

The two factors are 182 and -161, since:

$182\times (-161)=-31042$

$182-161=21$

Rewriting the equation with these factors:

$(b+182)(b-161)=0$

This yields two potential solutions for $b$:

$b=-182$ or $b=161$

Since breadth represents a physical distance, it cannot be negative. Therefore, we reject $b=-182$.

Thus, the breadth of the rectangular ground is 161 m.