A rectangle has a perimeter of 12 x +8y. If one side of the rectangle is 4x-2y. write and expression of the other side.
2(2x +y) is this right
No, that expression is not correct. To find the expression for the other side of the rectangle, we need to subtract the given side from the perimeter.
Given:
Perimeter of the rectangle = 12x + 8y
One side of the rectangle = 4x - 2y
To find the other side, we subtract the given side from the perimeter:
Other side = Perimeter - Given side
Other side = (12x + 8y) - (4x - 2y)
When we simplify the expression, we get:
Other side = 12x + 8y - 4x + 2y
Other side = 8x + 10y
To find the expression for the other side of the rectangle, we'll use the formula for the perimeter of a rectangle, which can be expressed as 2(length + width).
Let's start by substituting the given values into the formula:
12x + 8y = 2(length + width)
We know that one side of the rectangle is 4x-2y, so we can substitute it for either the length or the width. Let's assume it is the length.
12x + 8y = 2(4x - 2y + width)
To isolate the width, we need to isolate it from the constants and the other variables. Let's simplify the equation:
12x + 8y = 8x - 4y + 2width
Next, let's move the constant terms to one side and the variables to the other side:
12x - 8x + 4y + 4y = 2width
Simplifying further:
4x + 8y = 2width
Dividing both sides of the equation by 2:
2x + 4y = width
Therefore, the expression for the other side (width) of the rectangle is 2x + 4y.
Your suggestion of 2(2x + y) is close but not exactly correct.
check
half perimeter = 6 x + 4 y
is that
4 x - 2 y + 4 x + 2 y
no
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now
6 x + 4 y = 4 x - 2y + a x + b y
6 x = 4 x + a x
a = 2
4 y = - 2 y + b y
b = 6
so I get 2 x + 6 y
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check mine
6 x + 4 y = 4 x - 2 y + 2 x + 6 y ?????
6 x + 4 y = 6 x + 4 y ..........sure enough