Question

a rectangular field is 60 yards wide and 90 yards long. give the length and width of another rectangular field that has the same perimeter but a smaller area. width = yards length = yards

Explanation:

Step1: Calculate the perimeter of the original rectangle

The perimeter formula for a rectangle is $P = 2(l + w)$. For the given rectangle with $l = 90$ yards and $w = 60$ yards, $P=2(90 + 60)=2\times150 = 300$ yards.

Step2: Recall the relationship between length - width and area

The area formula of a rectangle is $A=l\times w$. For a fixed perimeter, the area is maximized when the rectangle is a square. As the difference between the length and the width increases, the area decreases. Let the new width be $w_1$ and length be $l_1$ such that $2(l_1 + w_1)=300$, or $l_1+w_1 = 150$.

Step3: Choose values for length and width

We can choose $w_1 = 10$ yards and $l_1=140$ yards. (There are multiple possible answers as long as $l_1 + w_1=150$ and $l_1
eq w_1$ and $l_1>0,w_1>0$).

Answer:

width = 10 yards
length = 140 yards