given H is the midpoint of GI. the length of GH is represented by 4x-5 and the length of HI is represented by 3x+20. find the value of x and the measures of GI, Gh, and HI.
To find the value of x and the measures of GI, GH, and HI, we can use the fact that H is the midpoint of GI. This means that the lengths GH and HI are equal.
Since GH = 4x - 5 and HI = 3x + 20, we can set up an equation:
4x - 5 = 3x + 20
To solve for x, we can subtract 3x from both sides of the equation:
4x - 3x - 5 = 3x - 3x + 20
Simplifying the equation, we have:
x - 5 = 20
Next, we add 5 to both sides of the equation:
x - 5 + 5 = 20 + 5
Simplifying further:
x = 25
So, x is equal to 25.
Now, we can substitute the value of x into the expressions for GH and HI to find their measures:
GH = 4x - 5 = 4(25) - 5 = 100 - 5 = 95
HI = 3x + 20 = 3(25) + 20 = 75 + 20 = 95
Thus, the measures are:
- x = 25
- GI = GH + HI = 95 + 95 = 190
- GH = 95
- HI = 95
To find the value of x and the measures of GH, HI, and GI, we can set up an equation based on the information given.
Given that H is the midpoint of GI, we know that GH is equal to HI. Therefore, we can set up the following equation:
4x - 5 = 3x + 20
To solve this equation for x, we will isolate the variable.
Subtract 3x from both sides of the equation:
4x - 3x - 5 = 3x - 3x + 20
x - 5 = 20
Next, add 5 to both sides of the equation:
x - 5 + 5 = 20 + 5
x = 25
Now that we have the value of x, we can substitute it into the expressions for GH and HI to find their lengths.
GH = 4x - 5
GH = 4(25) - 5
GH = 100 - 5
GH = 95
HI = 3x + 20
HI = 3(25) + 20
HI = 75 + 20
HI = 95
Therefore, the value of x is 25. The lengths of GH and HI are both 95 units, and the length of GI is their sum:
GI = GH + HI
GI = 95 + 95
GI = 190
The two parts are equal, so ...
4x-5 = 3x + 20
x = 25
so GH = 4x-5 = 4(25) - 5 = 95
HI = 3(25) + 20 = 95
I guess GI = 190