Question

a rectangular park is 50 meters wide and 80 meters long. give the length and width of another rectangular park that has the same perimeter but a smaller area. width = meters length = meters

Explanation:

Step1: Calculate the perimeter of the original park

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). For the given park with \(l = 80\) meters and \(w = 50\) meters, \(P=2(80 + 50)=2\times130 = 260\) meters.

Step2: Calculate the area of the original park

The formula for the area of a rectangle is \(A=l\times w\). So, \(A = 80\times50=4000\) square - meters.

Step3: Find new length and width with the same perimeter

Let the new width be \(w_1\) and new length be \(l_1\), such that \(2(l_1 + w_1)=260\), so \(l_1 + w_1=130\), or \(l_1=130 - w_1\). The area \(A_1=w_1\times(130 - w_1)=130w_1-w_1^{2}\).
We can try values. If \(w_1 = 30\) meters, then \(l_1=130 - 30=100\) meters.

Step4: Calculate the area of the new park

\(A_1=30\times100 = 3000\) square - meters. Since \(3000<4000\)

Answer:

width = \(30\) meters, length = \(100\) meters