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:

Problem 9

Step1: Set up the equation for AC

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

Step2: Simplify and solve for x

Combine like terms: \( 3x + 9 = 39 \). Subtract 9 from both sides: \( 3x = 30 \). Divide by 3: \( x = 10 \).

Step3: Find AB

Substitute \( x = 10 \) into \( AB = 2x - 8 \): \( AB = 2(10) - 8 = 12 \) m.

Step4: Find BC

Substitute \( x = 10 \) into \( BC = x + 17 \): \( BC = 10 + 17 = 27 \) m.

Step1: Set up the equation for DG

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

Step2: Simplify and solve for x

Combine like terms: \( 6x + 18 = 60 \). Subtract 18 from both sides: \( 6x = 42 \). Divide by 6: \( x = 7 \).

Step3: Find DO

Substitute \( x = 7 \) into \( DO = 4x - 3 \): \( DO = 4(7) - 3 = 25 \) ft.

Step4: Find OG

Substitute \( x = 7 \) into \( OG = 2x + 21 \): \( OG = 2(7) + 21 = 35 \) ft.

Answer:

\( x = 10 \), \( AB = 12 \) m, \( BC = 27 \) m

Problem 10