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

Let us solve this problem step-by-step by first finding the area of the rectangular field and then using it to determine the diagonal of the square plot.

Step 1: Calculate the area of the rectangular field.
The formula for the area of a rectangle is:

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

Given:
Length of the rectangular field ($l$) = 90 m
Breadth of the rectangular field ($b$) = 80 m

Substituting the given values:

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

Step 2: Relate the area of the rectangle to the square plot.
According to the problem statement, 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.
The area of a square can be expressed directly in terms of its diagonal ($d$) using the formula:

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

Substituting the area of the square into the formula:

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

Multiply both sides by 2:

$d^2=7200\times 2$

$d^2=14400$

Now, take the square root of both sides to find the length of the diagonal ($d$):

$d=\sqrt{14400}$

$d=120\text{m}$

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