The length of a rectangle is three times its width and length of its diagonal is 6√(10)cm.What is the perimeter?
To solve this problem, we need to start by finding the length and width of the rectangle. Let's assign the width as "w" and the length as "l".
1. The problem states that the length is three times the width: l = 3w.
2. We also know that the length, width, and diagonal of a rectangle form a right triangle. Using the Pythagorean theorem, we can find the relationship between the length, width, and diagonal:
l² + w² = diagonal²
(3w)² + w² = (6√10)²
9w² + w² = 360
10w² = 360
w² = 36
w = 6
3. Now that we have the width, we can substitute it back into the equation to find the length:
l = 3w
l = 3(6)
l = 18
So, the width of the rectangle is 6 cm, and the length is 18 cm.
To find the perimeter of the rectangle, we can use the formula: perimeter = 2(length + width).
Perimeter = 2(18 + 6)
Perimeter = 2(24)
Perimeter = 48 cm
Therefore, the perimeter of the rectangle is 48 cm.
width -- x
length -- 3x
so x^2 + (3x)^2 = (6√10)^2
10x^2 = 360
x^2 = 36
x = 6
finish it up