Question

The cost of levelling a square lawn at rupees 15 per square metre is 20535. Find the cost of fencing the lawn at rupees 22 per metre

chapter square and square roots ​

Answer 1

The cost of levelling the square lawn is Rs 19935 at Rs 15 per sq. metre.

ii) The rate of fencing the lawn is Rs 22 per metre.

From information (i) we can find the area of the square:

Rs 15 needed for levelling 1 square metre.

So, Rs 1 needed for levelling 1/15 square metre.

Hence Rs 19935 needed for levelling (19935/15) square metre. = 1329 square metre.

This will be the area of the square. That is the area of the square is 1329 square metre. ( There are two ways to understand that this will be the area of the square. One from looking at the units. Unit given is in square metre, which is the unit of area. Another hint is "levelling" the lawn. You level the surface of the lawn, giving us the area.)

From this area, we can calculate the side of the square.

Area of square = side * side = side^{2}side

2

Hence side of the square = \sqrt{area}

area

So a side of the square will be \sqrt{1329} = 36.455

1329

=36.455 (rounded to three decimal digits)

Now using the information (ii), we can find the cost of fencing the lawn.

To fence the lawn we need to cover the whole perimeter. So we need to find the perimeter of the square, which is 4 * (length of a side of the square).

Here perimeter is 4 * \sqrt{1329} 1329

.

And the total cost of fencing would be Rs 22 * 4 * \sqrt{1329} 1329

. = Rs 3208.08 (rounded off to two decimal numbers)

One Tip: If you are not doing calculations by hand, I would suggest not to round the values in intermediate steps. This is because you will get a minor deviation in the final answer. It is okay to round off in intermediate steps if you are doing calculations by hand.