If 16x+8y represents the perimeter of a rectangle, and 5x-2y reprents its width, then what is expression of lenght?
Perimeter = 2(Length + Width),so
length = (perimeter)/2 - Width
=(16x+8y)/2 - (5x-2y)
=8x+4y - (5x-2y)
= 3x+6y
Well, if we know that the perimeter is equal to 16x + 8y, and the width is given by 5x - 2y, then we can use a little math and humor to find the expression for the length. Let me calculate that for you.
Now, we know that the formula for the perimeter of a rectangle is the sum of all its sides. In this case, we have two sides with lengths 5x - 2y, and the other two sides must also have the same lengths to form a rectangle. So:
Perimeter = 2 * (Length + Width)
Replace the width with 5x - 2y:
16x + 8y = 2 * (Length + (5x - 2y))
Now, let's simplify this equation:
16x + 8y = 2 * Length + 10x - 4y
Now, let's gather the terms involving Length:
16x + 8y - 10x + 4y = 2 * Length
6x + 12y = 2 * Length
To find the expression for the length, divide both sides by 2:
3x + 6y = Length
And there you have it! The expression for the length of the rectangle is 3x + 6y. Now, go forth and calculate those dimensions with a smile!
To find the expression for the length of the rectangle, we need to subtract twice the width from the perimeter.
Given:
Perimeter = 16x + 8y
Width = 5x - 2y
To find Length:
Length = Perimeter - 2 * Width
Substituting the given values:
Length = (16x + 8y) - 2(5x - 2y)
Expanding the expression:
Length = 16x + 8y - 10x + 4y
Combining like terms:
Length = 6x + 12y
Therefore, the expression for the length of the rectangle is 6x + 12y.
To find the expression for the length of the rectangle, we first need to understand the relationship between the perimeter and the dimensions of a rectangle.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the given expression 16x + 8y represents the perimeter of the rectangle.
Now, let's consider the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
We know that the width is given by the expression 5x - 2y.
Substituting the given values into the formula, we have:
16x + 8y = 2(length + (5x - 2y))
To find the expression for the length, let's simplify the equation:
16x + 8y = 2(length + 5x - 2y)
Let's first distribute the 2 on the right side of the equation:
16x + 8y = 2(length) + 2(5x) - 2(2y)
Simplifying further:
16x + 8y = 2length + 10x - 4y
Now, let's collect similar terms:
16x + 8y - 10x + 4y = 2length
Simplifying again:
6x + 12y = 2length
Finally, we can divide both sides by 2 to solve for the length:
3x + 6y = length
Therefore, the expression for the length of the rectangle is 3x + 6y.