A rectangular plot of land has sides with lengt... - JAMB Mathematics 2023 Question

The area \(A\) of a rectangle is given by the formula \(A = \text{length} \times \text{width}\).

Given that the length is 38 m and the width is 52 m, we can calculate the area:

\[A = 38 \times 52\]

\[A = 1976 \, \text{m}^2\]

Now, let's consider the possible range of values for the area due to the measurements being correct to the nearest meter.

For the lower bound, we can calculate the area using the lower limits of the lengths:

\[A_{\text{lower}} = (38 - 0.5) \times (52 - 0.5)\]

\[A_{\text{lower}} = 37.5 \times 51.5\]

\[A_{\text{lower}} = 1931.25 \, \text{m}^2\]

For the upper bound, we can calculate the area using the upper limits of the lengths:

\[A_{\text{upper}} = (38 + 0.5) \times (52 + 0.5)\]

\[A_{\text{upper}} = 38.5 \times 52.5\]

\[A_{\text{upper}} = 2021.25 \, \text{m}^2\]

Therefore, the range of possible values for the area is \(1931.25 \, \text{m}^2 \leq A < 2021.25 \, \text{m}^2\).

So, the correct answer is \(1931.25 \, \text{m}^2 \leq A < 2021.25 \, \text{m}^2\)