A rectangle has length and width in the ratio of 5:9. If the perimeter is 280, what is the length of the rectangle?
let the width be 5x and the length 9x
P = 2l + 2w = 10x + 18x = 28x
28x = 280
x = 10
width is 50, length is 90
To solve this problem, we can set up a proportion using the ratio of the length and width.
Let's assume the length of the rectangle is 5x, and the width is 9x.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Plugging in the values, we get:
280 = 2(5x) + 2(9x)
Simplifying the equation, we have:
280 = 10x + 18x
Combining like terms, we get:
280 = 28x
Dividing both sides by 28, we find:
x = 10
Now, we can find the length of the rectangle by plugging the value of x back into the equation:
Length = 5x = 5(10) = 50
Therefore, the length of the rectangle is 50.
To find the length of the rectangle, let's start by setting up a ratio.
The ratio of length to width is given as 5:9.
Let's assign a variable to the common ratio between the length and width. We can call it "x".
So, the length of the rectangle can be represented as 5x, and the width can be represented as 9x.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
In this case, the perimeter is given as 280, so we can write the equation as: 280 = 2(5x + 9x).
Simplifying the equation:
280 = 2(14x)
Divide both sides of the equation by 2 to isolate "14x":
140 = 14x.
Now, divide both sides of the equation by 14 to solve for "x":
x = 140/14 = 10.
Since the length of the rectangle is represented as 5x, we can substitute the value of "x" back into the equation:
Length = 5 * 10 = 50.
Therefore, the length of the rectangle is 50 units.