Quadrilateral RSTU is a rectangle with diagonal RT. If m = 8x + 4 and = 3x – 2, find x.
the answer is x= 8
To find the value of x, we can set the expressions for the measures of the diagonals equal to each other.
Given:
Measure of diagonal RT = m = 8x + 4
Measure of diagonal SU = n = 3x - 2
Since these diagonals are equal in a rectangle, we can set them equal to each other:
8x + 4 = 3x - 2
To solve for x, we can now manipulate this equation:
8x - 3x = -2 - 4
Combine like terms:
5x = -6
Divide both sides of the equation by 5:
x = -6/5
Therefore, x is equal to -6/5.
To find the value of x, we will use the fact that the diagonals of a rectangle are equal in length. Given that the diagonal RT has a measure of 8x + 4 and the diagonal SU has a measure of 3x - 2, we can set up an equation:
8x + 4 = 3x - 2
To solve for x, we need to isolate the variable on one side of the equation. Let's start by getting rid of the constant terms on both sides:
8x - 3x = -2 - 4
Simplifying further:
5x = -6
Now, we can solve for x by dividing both sides of the equation by 5:
x = -6 / 5
Therefore, the value of x is -6/5.