1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mixer [17]
3 years ago
13

In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈CM and a line AP intersecting BC at point Q. Find

the lengths of segments CQ and BQ, if P divides CM into CP:PM=1:2.

Mathematics
1 answer:
defon3 years ago
6 0

Answer:

  • CQ = 2.4 cm
  • BQ = 9.6 cm

Step-by-step explanation:

This development is ugly, but it works.

Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.

Let area ΔCPQ = x. Then ...

... area ΔACQ = area ΔAPC + area ΔCPQ

... area ΔACQ = a + x

Define k such that BQ : CQ = k : 1. Then ...

... area ΔBPQ + area ΔCPQ = area ΔBPC

... kx + x = a = (k +1)x

The division of BC into parts of ratio k : 1 means ...

... area ΔABQ = k × area ΔACQ

... area ΔABQ + area ΔACQ = area ΔABC

... k × area ΔACQ + area ΔACQ = area ΔABC

... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a

... (k +1)x +(k +1)a = 6a . . . . . distributive property

... a + (k +1)a = 6a

... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify

... k = 4

Now, we know BQ : CQ = 4 : 1, so ...

... BQ = 4/5 × 12 cm = 9.6 cm

... CQ = 1/5 × 12 cm = 2.4 cm

You might be interested in
maximize P=9x+9y Subject to 2x+y is less than or equal to 30 x+2y is less than or equal to 24 x, y is greater than 0 What is the
Inga [223]
Find the intersection point between the 2 restraint equations:
30 - 2x = 12 - \frac{1}{2} x  \\ \frac{3}{2} x = 18  \\  x = 12

Substitute back in to find y-value:
y = 30 - 2(12) = 6

P is maximized at point (12,6)
P = 9(12)+9(6) = 162
3 0
3 years ago
name the set of 6 consecutive integers starting with -3 put the set in braces and put commas between the elements of the set
melisa1 [442]
6-3=3 that is the answer ok
6 0
3 years ago
The average of five numbers is 85. If each of the numbers is increased by 4, what is the average of the five new numbers?
velikii [3]

Answer:

21.25!!!

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What are Two equations that model this relationship 5:25
JulijaS [17]

Answer:

5/25 and 5 to 25

Step-by-step explanation:

jssjskkdkddk

8 0
3 years ago
Which is the most accurate way to estimate 49% of 49
Svetlanka [38]

Answer:

49% of 49 is 24.01

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Help please and thank you
    11·1 answer
  • Whats 15/20 simplafide to
    8·2 answers
  • There are 72 boys and 28 girls. What percent are girls? I'm not sure if it is 28% or 18%?
    10·1 answer
  • What is the means-to-MAD ratio of the two data sets, expressed as a decimal?
    6·1 answer
  • Have a question!!! Need help!!!!!! Are these correct???? Or Not????
    5·1 answer
  • I need helppppppppppppp
    5·1 answer
  • Help me plz It’s due now
    14·2 answers
  • Describe what slope is and what the numerator and denominator represent for slope (such as 3/4). Give 2 examples of where slope
    12·1 answer
  • 10.Adrienne is going to deposit $8,500 in an account that earns 2.5% interest for 360 months. How much more interest will she ea
    6·1 answer
  • Mike owes his friend $6. Each day, Mike earns $3 per day.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!