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
Why does (-5) (-5) (-5) have a negative product?
Lorico [155]

Answer:

Yes, -125

Step-by-step explanation:

4 0
3 years ago
Louis made 24 quarts of lemonade he divided the lemonade equally between 6 pitchers how many points of lemonade did Louis put in
Mandarinka [93]

Answer: Each pitcher has 4 quarts of lemonade.

Step-by-step explanation:

Louis made 24 quarts of lemonade, and he divided it equally into 6 pitchers.

Then, each pitcher must has a sixt of the total amount of lemonade, this is:

p = (1/6)*24 quarts= (24/6) quarts = 4 quarts

Each pitcher has 4 quarts of lemonade.

7 0
3 years ago
Read 2 more answers
Martha Washington walks 30 minutes each day. If she walks for 140 days, how many hours will she walk?
telo118 [61]

70

make 30 minutes into an hour then divide 140 by 2

140/2=70

70x1=70

5 0
2 years ago
How does solving the equation arithmetically compare to solving an equation algebraically
IRISSAK [1]
In an arithmetic equation, there is no variable in the 'meat' of the equation(example: 5-5=0). In an algebraic equation, there is a variable in the meat of the equation(example: 5-x=0).
Hope this helps and please give brainliest!
4 0
3 years ago
At the beach, 49% of people have red towels and 11% have blue towels. If the
Margaret [11]

Answer: 40%

Step-by-step explanation:

Percentage of people that have red towels = 49%

Percentage of people that have blue towels = 11%

Therefore, the percentage of the people at the beach have white

towels will be:

= 100% - (49% + 11%)

= 100% - 60%

= 40%

Therefore, the answer is 40%.

3 0
3 years ago
Other questions:
  • What is the base of a triangle with an area of 36 square centimeters and a height of 9 centimeters?
    8·2 answers
  • Nine more than the product of 23 and mabel’s savings
    9·1 answer
  • There is more than one integer greater than 1 which leaves a reminder of1 when divided by each of the four smallest primes
    5·1 answer
  • What is the solution to the division problem? Enter numbers in the boxes to complete the problem.​
    11·2 answers
  • If Melanie spins this spinner 1000 times, approximately how many times will it land on orange?
    9·2 answers
  • The measures of the acute angles of a right triangle are in the ratio 5:7
    7·1 answer
  • Ratios for 42 and 54
    13·2 answers
  • Subtract 9a from -15a
    12·2 answers
  • Please help I’ll give brainliest
    9·1 answer
  • How many lines of symmetry does this figure have​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!