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
marissa [1.9K]
3 years ago
11

In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is

30. what is the measure of ad?

Mathematics
2 answers:
Musya8 [376]3 years ago
4 0
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
Mrac [35]3 years ago
4 0
See the attachment....

You might be interested in
Which variable is ordinal?​
Leviafan [203]

Answer:

Categorical variable

Step-by-step explanation:

An ordinal variable is a categorical variable for which the possible values are ordered. Please mark me as brainliest.

6 0
2 years ago
Arrange these numbers in order from least to greatest 0.1, 1, -1,
LenaWriter [7]

Answer:

-1, 0.1, 1

•••••••••••••

3 0
3 years ago
Read 2 more answers
What is the answer of. 4y+7>-x-3
lora16 [44]
I don’t know what u need to look for but I think for y
4y+7>-x-3
4y>-x-10
y>-1/4x-5/2
5 0
3 years ago
A man gave half of his welfare allowance to his wife,1/5 to each of his two sons the rest to his daughter. Find the fraction giv
vichka [17]

Answer:

1/10.

Step-by-step explanation:

Total allowance=1

Half to wife so 1-1/2=1/2(Left from total)

1/5 to each son so 2/5 to both(Total for sons).

Left for daughter 1/2-2/5=1/10(Ans)

8 0
3 years ago
PLEASE HELP THIS IS DUE ASAP!!!!!
just olya [345]

Answer:

101

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • 30 is 12.5% of what number?
    7·2 answers
  • An equation was used to predict the number of possible enrollments in an afterschool program for the first 6 months of the year.
    13·1 answer
  • Please help it’s really important because if I get it wrong I have to restart.
    13·1 answer
  • Which description of the graph of the linear equality y > 3x - 8 is correct?
    5·2 answers
  • What is the 43rd term of the sequence: 17, 9, 1, -7
    9·1 answer
  • Which fraction equals the ratio of rise to run between the points (0, 0) and (6, 7)? A. B. C. D.
    5·1 answer
  • 1. In the diagram below, AB = AC, CB = CE,<br> BD = BE, BC = 9 cm and CD = 5 cm. FindAC.
    5·1 answer
  • Crazy Valentine's day Work sheet. SOOOO CONFUSEDDD! Answered 1 and 3.
    6·1 answer
  • PLESSS PLESS PLESSSSSSS I BEG OF YOU TEACH ME HOW TO DO THISSSS I BEGG I WILL GIVE BRAINYLIST TO ANYONE WHO ANSWERS PLESS I CRY
    12·1 answer
  • Please help!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!