Question

ASAP!! PLEASE I NEED HELP!!

A farmer needs to fence a rectangular plot of land with the area of 3000 square yards. He considers several possible length of the plot: 50 yards, 40 yards, 48 yards, and 36 yards. What will be the width of the plot in each case? Do the length and the width of the rectangular plot vary directly or inversely when the same area is needed? Explain why.
Answer:
If the length is 50 yd, the width is
yd.
If the length is 40 yd, the width is
yd.
If the length is 48 yd, the width is
yd.
If the length is 36 yd, the width is
yd.
The length and the width vary .

Answer 1

To find the width of a rectangular plot, divide the area by the length. The length and width of the plot vary inversely when the same area is needed.

Step-by-step explanation:

The width of the rectangular plot can be calculated by dividing the area by the length. To find the width for each length:

1. For a length of 50 yards, the width is 3000/50 = 60 yards.
2. For a length of 40 yards, the width is 3000/40 = 75 yards.
3. For a length of 48 yards, the width is 3000/48 = 62.5 yards.
4. For a length of 36 yards, the width is 3000/36 = 83.33 yards (rounded to two decimal places).

The length and the width of the rectangular plot vary inversely when the same area is needed. This means that as the length increases, the width decreases to maintain the same area. This relationship can be seen in the calculations above, where a longer length results in a smaller width.

Answer 2

If the length is 50 yd, the width is 60 yd.

If the length is 40 yd, the width is 75 yd.

If the length is 48 yd, the width is 62.5 yd.

If the length is 36 yd, the width is 83.33 yd.

The length and the width vary inversely because when the length decreased the width increased

Step-by-step explanation:

The area of any rectangle A = L × W, where

• L is its length
• W is its width

The relation is direct proportion if the quotient of two quantity equals constant (y/x = k, when y and x increased) and inverse if the product of the two quantity equals constant (yx = k, when x increased y decreased and vice versa)

∵ The area of the rectangular plot of land = 3000 yards²

∴ A = 3000

∵ Its length = 50 yards

∴ L = 50

→ Substitute them in the rule above to find W

∵ 3000 = 50 × W

→ Divide both sides by 50 to find W

∴ 60 = W

∴ The width of the plot is 60 yards

∵ Its length = 40 yards

∴ L = 40

→ Substitute them in the rule above to find W

∵ 3000 = 40 × W

→ Divide both sides by 40 to find W

∴ 75 = W

∴ The width of the plot is 75 yards

∵ Its length = 48 yards

∴ L = 48

→ Substitute them in the rule above to find W

∵ 3000 = 48 × W

→ Divide both sides by 48 to find W

∴ 62.5 = W

∴ The width of the plot is 62.5 yards

∵ Its length = 36 yards

∴ L = 36

→ Substitute them in the rule above to find W

∵ 3000 = 36 × W

→ Divide both sides by 36 to find W

∴ 83. 33 = W

∴ The width of the plot is 83.33 yards

∵ The area is a constant value

∵ A = LW

→ The product of L and W equals the constant value, can you discover

that from the values of L and W

∴ The length and the width of the rectangular plot vary inversely