Question

a rectangular lot is 110 yards long and 75 yards wide. give the length and width of another rectangular lot 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 a rectangle with $l = 110$ yards and $w = 75$ yards, $P=2(110 + 75)=2\times185 = 370$ yards.

Step2: Recall the property of rectangle - area and perimeter relationship

For a given perimeter, a rectangle with sides that are more different in length will have a smaller area. Let the new length $l_1$ and width $w_1$ such that $2(l_1 + w_1)=370$, or $l_1 + w_1 = 185$.
Let's choose $l_1=150$ yards, then $w_1=185 - 150=35$ yards.

Answer:

width = 35 yards
length = 150 yards