The length of the rectangle whose perimeter is 192 feet, and the length is 3 times its width, is 72 feet.
Also, its width is 24 feet.
The perimeter of an object is the total length of its boundary.
The perimeter of a rectangle is the sum of its sides. We know that a rectangle has two lengths and two breadths. Adding them, we get the formula for the perimeter of a rectangle:
Perimeter of rectangle = 2(length + breadth)
In the question, we are asked to find the length of the rectangle whose perimeter is 192 feet, and the length is 3 times its width.
To find the length, we will try to make a linear equation and then solve it.
We assume the width of the rectangle to be x feet.
∴ The length of the rectangle is 3 times its width, so the length = 3x feet.
By the formula for the perimeter of a rectangle, we know that:
Perimeter of rectangle = 2(length + breadth)
or, 192 = 2(3x + x)
or, 2(3x + x) = 192 (changing sides)
or, 2(4x) = 192 (Adding 3x and x)
or, 8x = 192 (Simplifying the parenthesis)
or, 8x/8 = 192/8 (Dividing both sides by 8)
or, x = 24 (Simplifying).
∴ The width of the rectangle = 24 feet.
∴ The length of the rectangle = 3*24 feet = 72 feet.
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