Question

given: dg = 60 ft. d 4x - 3 o 2x + 21 g use the diagram and segment addition postulate to set up an equation and find the requested values. sketch your thinking in the box. (note: the diagram is not to scale.)

Explanation:

Step1: Apply segment - addition postulate

Since $DG=DO + OG$ and $DG = 60$, $DO=4x - 3$, $OG=2x + 21$, we have the equation $(4x - 3)+(2x + 21)=60$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $4x+2x-3 + 21=60$, which simplifies to $6x+18 = 60$.

Step3: Solve for $x$

Subtract 18 from both sides: $6x=60 - 18$, so $6x=42$. Then divide both sides by 6: $x=\frac{42}{6}=7$.

Step4: Find the length of $DO$

Substitute $x = 7$ into the expression for $DO$: $DO=4x-3=4\times7-3=28 - 3=25$ ft.

Step5: Find the length of $OG$

Substitute $x = 7$ into the expression for $OG$: $OG=2x + 21=2\times7+21=14 + 21=35$ ft.

Answer:

$x = 7$
$DO=25$ ft
$OG = 35$ ft