The area of rectangular field of length 90 m and breadth 80 m is equal to the area of a square plot. What will be the length of the diagonal of the square plot?

Correct Answer: 120 m

Step-by-Step Explanation:

Step 1: Calculate the area of the rectangular field

The length (l) of the rectangular field is given as 90 m and the breadth (b) is 80 m.

The formula for the area of a rectangle is:

$\text{Area of rectangle}=\text{length}\times \text{breadth}$

$\text{Area of rectangle}=90\text{ m}\times 80\text{ m}=7200{\text{ m}}^2$

Step 2: Relate the area of the rectangle to the area of the square plot

According to the question, the area of the rectangular field is equal to the area of the square plot.

$\text{Area of square plot}=7200{\text{ m}}^2$

Step 3: Calculate the length of the diagonal of the square plot

Let the side of the square plot be a and its diagonal be d.

The area of a square in terms of its side is:

$\text{Area}=a^2=7200$

The relation between the side a and the diagonal d of a square is given by Pythagoras theorem:

$d=a\sqrt{2}$

Squaring both sides gives:

$d^2=2a^2$

Alternatively, the area of a square in terms of its diagonal is given by:

$\text{Area}=\frac{1}{2}{d}^2$

Substituting the given area into the formula:

$7200=\frac{1}{2}{d}^2$

$d^2=7200\times 2$

$d^2=14400$

$d=\sqrt{14400}$

$d=120\text{ m}$

Thus, the length of the diagonal of the square plot is 120 m.