The length of a rectangle is three times its width and length of its diagonal is 6√(10)cm.What is the perimeter?

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To find the perimeter of a rectangle, we need to determine the lengths of its sides.

Let's assume the width of the rectangle is x cm.

Given that the length of the rectangle is three times its width, we can express the length as 3x cm.

We can use the Pythagorean theorem to relate the length, width, and diagonal of the rectangle. The theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides (the length and width).

Using the Pythagorean theorem, we can set up the following equation:

(width)^2 + (length)^2 = (diagonal)^2

x^2 + (3x)^2 = (6√10)^2

Simplifying the equation, we have:

x^2 + 9x^2 = 360

10x^2 = 360

Dividing both sides by 10:

x^2 = 36

Taking the square root of both sides:

x = 6

Therefore, the width of the rectangle is 6 cm, and the length is 3 * 6 = 18 cm.

To find the perimeter, we add up the lengths of all four sides:

Perimeter = 2*(width + length)
Perimeter = 2*(6 + 18)
Perimeter = 2*(24)
Perimeter = 48 cm

Therefore, the perimeter of the rectangle is 48 cm.