Find the dimensions of the rectangle meeting the specified conditions.
The perimeter is 20.4 millimeters and the length is 2.4 times the width. (Round your answers to one decimal place.)
width mm
length mm
well, you have
2(w + 2.4w) = 20.4
Now just solve for w, and the length is 2.4 times that.
Let's assume the width of the rectangle is x mm. Since the length is 2.4 times the width, the length would be 2.4x mm.
The perimeter of a rectangle is given by the formula: P = 2(length + width)
Given that the perimeter is 20.4 mm, we can write the equation:
20.4 = 2(2.4x + x)
Simplifying the equation:
20.4 = 2(3.4x)
20.4 = 6.8x
x = 20.4 / 6.8
x ≈ 3 mm
So, the width of the rectangle is approximately 3 mm.
The length of the rectangle can be found by multiplying the width by 2.4:
length = 2.4 * 3
length = 7.2 mm
Therefore, the dimensions of the rectangle are:
width = 3 mm
length = 7.2 mm
To find the dimensions of the rectangle, we can set up a system of equations based on the given conditions.
Let's suppose the width of the rectangle is "w" millimeters.
According to the condition, the length of the rectangle is 2.4 times the width, so the length would be 2.4w millimeters.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter is 20.4 millimeters, we can substitute the values into the formula:
20.4 = 2(2.4w + w)
Simplifying the equation:
20.4 = 2(3.4w)
20.4 = 6.8w
To solve for w, divide both sides of the equation by 6.8:
w = 20.4 / 6.8
w ≈ 3
Now that we have the value of the width, we can find the length by multiplying it by 2.4:
length = 2.4 * 3
length ≈ 7.2
Therefore, the dimensions of the rectangle are approximately:
width = 3 mm
length = 7.2 mm