Question

On section AB, whose length is 192 cm, take the point C so that AC: CB = 1: 3. The point D is taken on the AC section so that CD = BC / 12. Find the distance between the midpoints of the AD and CB sections

50 points

Answer 1

• 112 cm

Explanation:

Given:

• AB = 192 cm
• AC : CB = 1 : 3
• CD = BC/12
• The distance between midpoints of AD and CB = x

Find the length of AC and CB:

• AC + CB = AB
• AC + 3AC = 192
• 4AC = 192
• AC = 192/4
• AC = 48 cm

Find CB:

• CB = 3AC = 3*48 = 144 cm

Find the length of CD:

• CD = BC/12 = 144/12 = 12 cm

Find the length of AD:

• AD = AC - CD = 48 - 12 = 36 cm

Find the midpoint of AD:

• m(AD) = 36/2 = 18 cm

Find the midpoint of CB:

• m(CB) = AC + 1/2CB = 48 + 144/2 = 48 + 82 = 130 cm

Find the distance between the midpoints:

• x = 130 - 18 = 112 cm