the length and breadth of the room were measured and area calculated as 600sq.m. (l+B=50) later found the meter rod that had used as an error 5cm i.e actual length of the rod ws 95cm instead of 100cm. find the correct area of the room

The room was measured to be 20 by 30 m.

So, just multiply each dimension by 0.95 to find the true area.

Or, just do it in one step: 600 * 0.95^2

To find the correct area of the room, we can use the formula for the area of a rectangle, which is the product of its length and breadth.

Let's denote the length of the room as "L" and the breadth of the room as "B".

According to the given information, the sum of the length and breadth is 50 (L + B = 50), and the area of the room is 600 sq.m. (L * B = 600).

Since we know the length of the meter rod used to measure the room was incorrect, we need to adjust the measurements accordingly.

The error in the length of the rod is 5 cm, which means the actual length of the room (L) should be 95 cm instead of 100 cm.

We can now solve the above two equations using substitution.

Substituting the value of L from the first equation into the second equation, we have:

(50 - B) * B = 600

Expanding the equation, we get:

50B - B^2 = 600

Rearranging the equation, we have:

B^2 - 50B + 600 = 0

This equation is a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring the equation, we get:

(B - 20)(B - 30) = 0

So, either B - 20 = 0 or B - 30 = 0.

If B - 20 = 0, then B = 20. If B - 30 = 0, then B = 30.

Now we can find the corresponding values of L using the equation L + B = 50.

If B = 20, then L = 30.
If B = 30, then L = 20.

Since the length cannot be greater than the breadth for a room, we can conclude that the correct dimensions of the room are L = 30 m and B = 20 m.

Finally, we can calculate the correct area of the room by multiplying the correct dimensions:

Correct Area = L * B = 30 m * 20 m = 600 sq.m.

Therefore, the correct area of the room is 600 square meters.