Question

a rectangular field is 85 yards wide and 125 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 of a rectangle is $P = 2(l + w)$. For a rectangle with length $l = 125$ yards and width $w = 85$ yards, $P=2(125 + 85)=2\times210 = 420$ yards.

Step2: Recall the property of rectangle area

The area of a rectangle is $A=l\times w$. For a fixed - perimeter rectangle, the closer the length and width are to each other, the larger the area. To get a smaller area with the same perimeter, we need to increase the difference between the length and the width.
Let the width be $w_1 = 10$ yards. Then, since $P = 2(l_1+w_1)=420$, we have $l_1+w_1 = 210$. Substituting $w_1 = 10$ into the equation, we get $l_1=210 - 10=200$ yards.

Answer:

width = 10 yards
length = 200 yards