Question

a rectangular park is 100 meters long and 50 meters wide. 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 perimeter formula for a rectangle is \(P = 2(l + w)\). For the original park with \(l = 100\) meters and \(w = 50\) meters, \(P=2(100 + 50)=300\) meters.

Step2: Express the relationship between length and width for the new park

Let the new length be \(x\) and new width be \(y\). Then \(2(x + y)=300\), so \(x + y=150\), and \(y = 150 - x\).

Step3: Calculate the area of the new park

The area formula is \(A=xy=x(150 - x)=150x - x^{2}\). The area of the original park is \(A_{original}=100\times50 = 5000\) square - meters.
We can try values. If \(x = 140\) (length), then \(y=10\) (width) (since \(x + y = 150\)).
The area of the new park \(A_{new}=140\times10=1400\) square - meters.

Answer:

width = \(10\) meters, length = \(140\) meters