Answer:
Length = 50 ft
Width = 15 ft
Area = 750 ft²
Explanation:
Define the variables:
- Let W be the width of the rectangle.
- Let L be the length of the rectangle.
Create two equations with the given information.
Given:
- Three times the length is equal to 10 times the width.
⇒ 3L = 10W
Given:
- The perimeter of the rectangle is 130 ft.
⇒ 2W + 2L = 130
Rearrange the second equation to make W the subject:
⇒ 2(W + L) = 130
⇒ W + L = 65
⇒ W = 65 - L
Substitute this into the first equation and solve for L:
⇒ 3L = 10(65 - L)
⇒ 3L = 650 - 10L
⇒ 13L = 650
⇒ L = 50
Substitute the found value of L into the second equation and solve for W:
⇒ 2W + 2(50) = 130
⇒ 2W + 100 = 130
⇒ 2W = 30
⇒ W = 15
Therefore:
- Length of the rectangular pool = 50 ft
- Width of the rectangular pool = 15 ft
Substitute the found values of W and L into the formula for area of a rectangle to find the area of the pool:
⇒ Area = W × L
⇒ Area = 15 × 50
⇒ Area = 750 ft²