Question

arithmetic and algebra review
areas of rectangles with the same perimeter
a rectangular park is 105 yards long and 70 yards wide.
give the length and width of another rectangular park that has the same perimeter but a smaller area.
width = yards
length = yards

Explanation:

Step1: Calculate the perimeter of the first - park

The perimeter formula of a rectangle is $P = 2(l + w)$. For the first park with $l = 105$ yards and $w = 70$ yards, $P=2(105 + 70)=2\times175 = 350$ yards.

Step2: Recall the property of rectangle area

The area formula of a rectangle is $A=l\times w$. For a fixed perimeter, the closer the length and width are to each other, the larger the area. We want a rectangle with the same perimeter but a smaller area, so we can make the difference between length and width larger.
Let's assume the length $l = 150$ yards. Since $P = 2(l + w)=350$ yards, then $350=2(150 + w)$. Solving for $w$:
First, divide both sides of the equation by 2: $175=150 + w$.
Then subtract 150 from both sides: $w=175 - 150=25$ yards.

Answer:

width = 25 yards
length = 150 yards