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QuestionFind GHG H given that GH=13(x−1)G H=13(x-1), IG=16+4xI G=16+4 x, and HI=25H I=25.

Studdy Solution

STEP 1

Assumptions1. Point $$ is between Points $G$ and $H$. . The length of segment $GH$ is $13(x-1)$.
3. The length of segment $IG$ is $16+4x$.
4. The length of segment $HI$ is $25$.

STEP 2

Since point $$ is between points $G$ and $H$, the length of segment $GH$ is equal to the sum of the lengths of segments $IG$ and $HI$.
GH=IG+HIGH = IG + HI

STEP 3

Plug in the given values for GHGH, IGIG, and HIHI.
13(x−1)=16+x+2513(x-1) =16+x +25

STEP 4

implify the right side of the equation.
13(x−1)=4x+4113(x-1) =4x +41

STEP 5

istribute the13 on the left side of the equation.
13x−13=4x+4113x -13 =4x +41

STEP 6

Subtract 4x4x from both sides of the equation to isolate xx on one side.
13x−4x=41+1313x -4x =41 +13

STEP 7

implify both sides of the equation.
9x=549x =54

STEP 8

Divide both sides of the equation by to solve for xx.
x=54/x =54 /

STEP 9

Calculate the value of xx.
x=6x =6

STEP 10

Now that we have the value of xx, we can substitute it back into the expression for GHGH to find the length of segment GHGH.
GH=13(x−)GH =13(x-)

STEP 11

Substitute x=6x =6 into the equation.
GH=13(6−)GH =13(6-)

STEP 12

implify the expression inside the parentheses.
GH=(5)GH =(5)

STEP 13

Calculate the length of segment GHGH.
GH=65GH =65The length of segment GHGH is65 units.

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