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
Darina [25.2K]
3 years ago
14

Given: △ACM, m∠C=90°, CP ⊥ AM

Mathematics
1 answer:
larisa86 [58]3 years ago
8 0

Answer:  The answer is 3\dfrac{4}{7}.

Step-by-step explanation:  Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.

Now,

AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)

Comparing equations (A) and (B), we have

5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.

Thus,

AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.

You might be interested in
What is the volume (in cubic units) of a cylinder with a radius of
Contact [7]
It would be 339.1 hope this helps
4 0
2 years ago
Help the smol bean smol bean is stuggling
ruslelena [56]
Im confused can you please clarify?
5 0
3 years ago
Please its worth 20 points I will give you brainliest!!!​
trapecia [35]

Answer:

you can use desmos or symbolab

Step-by-step explanation:

5 0
3 years ago
What numbers to put in the table
alexandr1967 [171]
The missing numbers for distance are 9 and 20

The missing numbers for time are 12 and 48

(im going left to right)
4 0
3 years ago
Read 2 more answers
Are positive integers closed under subtraction?
Galina-37 [17]
Do you remember the answer..? I need help as well.
8 0
3 years ago
Read 2 more answers
Other questions:
  • V(t)=27,500(0.90)t. Find the value after 11 years
    14·1 answer
  • The student council had a canned food drive. They collected a total a total of 63 cans on Wednesday. This is 21% of the total ho
    14·1 answer
  • 1.<br> Which image is a reflection of the figure shown over the given line of<br> reflection?
    8·2 answers
  • Which expressions are differences of squares?
    10·1 answer
  • 1 point
    5·1 answer
  • Please help on my hw, I'm not feeling good, and can't concentrate
    15·1 answer
  • Pls help I’ll give 23 points
    13·1 answer
  • Party supplies inc. sells metallic balloons for $2 each and helium balloons for $3.50 per bunch. Yesterday, they sold 36 more me
    11·1 answer
  • 16 - 2 to the 3rd power over 16
    5·2 answers
  • At a football game 43% of people attending are supporting the home team while 57% we’re supporting the visiting team if the tota
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!