Respuesta :
Answer:
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
The length and the width of the rectangular plot vary inversely when the same area is needed.
Area of Rectangle:
Area of rectangular plot [tex]=length *width[/tex]
Given that, Area of plot is 3000 square yards.
- If the length is 50 yards. Then,
[tex]width=\frac{3000}{50} =60yd[/tex]
- If the length is 40 yards. Then,
[tex]width=\frac{3000}{40}=75yd[/tex]
- If the length is 48 yards. Then,
[tex]width=\frac{3000}{48}=62.5yd[/tex]
- If the length is 36 yards. Then,
[tex]width=\frac{3000}{36}=83.34yd[/tex]
Learn more about the area of rectangle here:
https://brainly.com/question/25292087
