Question

refer to the figure and the given information to find each measure.

1. given: ac = 39 m

a 2x - 8 b x + 17 c
x =
ab =
bc =

1. given the figure and dg = 60 ft.

d o g
4x - 3 2x + 21
x =
do =
og =

Explanation:

Step1: Set up equation for problem 9

Since $AC = AB + BC$ and $AC = 39$, $AB=2x - 8$, $BC=x + 17$, we have $(2x - 8)+(x + 17)=39$.

Step2: Simplify the left - hand side

Combine like terms: $2x-8+x + 17=3x+9$. So, $3x + 9=39$.

Step3: Solve for x

Subtract 9 from both sides: $3x=39 - 9=30$. Then divide both sides by 3, $x = 10$.

Step4: Find AB

Substitute $x = 10$ into $AB=2x - 8$, $AB=2\times10 - 8=12$ m.

Step5: Find BC

Substitute $x = 10$ into $BC=x + 17$, $BC=10 + 17=27$ m.

Step6: Set up equation for problem 10

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

Step7: Simplify the left - hand side

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

Step8: Solve for x

Subtract 18 from both sides: $6x=60 - 18 = 42$. Then divide both sides by 6, $x = 7$.

Step9: Find DO

Substitute $x = 7$ into $DO=4x - 3$, $DO=4\times7 - 3=25$ ft.

Step10: Find OG

Substitute $x = 7$ into $OG=2x + 21$, $OG=2\times7+21=35$ ft.

Answer:

Problem 9:
$x = 10$
$AB = 12$ m
$BC = 27$ m
Problem 10:
$x = 7$
$DO = 25$ ft
$OG = 35$ ft