Line LM is the mid-segment of rectangle ABCD. AB=x+8, LM = 4x+3, and DC=243. What is the value of x?
To find the value of x, we can use the fact that line LM is the mid-segment of rectangle ABCD.
In a rectangle, the mid-segment is half the length of the longer side.
Therefore, we can set up the following equation:
LM = (1/2) * DC
Substituting the given values, we have:
4x + 3 = (1/2) * 243
To solve for x, we need to isolate it on one side of the equation.
Let's multiply both sides of the equation by 2 to remove the fraction:
2 * (4x + 3) = 2 * (1/2) * 243
This simplifies to:
8x + 6 = 243
Next, subtract 6 from both sides of the equation:
8x = 243 - 6
Simplifying further:
8x = 237
To solve for x, divide both sides of the equation by 8:
x = 237 / 8
Now we can calculate the value of x:
x = 29.625
So the value of x is approximately 29.625.
To find the value of x, we can set up an equation using the information given.
In a rectangle, the mid-segment (LM) is equal to half the length of the longer side (DC).
So, we have:
LM = (1/2) * DC
Substituting the given values:
4x + 3 = (1/2) * 243
First, let's simplify the equation by multiplying both sides by 2:
2 * (4x + 3) = 243
8x + 6 = 243
Next, let's isolate x by subtracting 6 from both sides:
8x = 243 - 6
8x = 237
Finally, divide both sides by 8 to solve for x:
x = 237 / 8
x ≈ 29.625
Therefore, the value of x is approximately 29.625.