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
Dimas [21]
3 years ago
5

In △ABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . Find the length of DE if perimeter of ABDE is 30 cm and AB

= 12 cm

Mathematics
2 answers:
-BARSIC- [3]3 years ago
8 0

Answer:

DE = 6 cm

Step-by-step explanation:

Let DE = x cm.

Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)

As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.

Therefore, from (1) We get ,  m∠EAD = m∠ADE and m∠EBD = m∠BED.

So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.

So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then

12 + x + x + x = 30

⇒ 12 + 3x = 30

⇒ x = 6

Hence, the length of DE is 6 cm.


Romashka-Z-Leto [24]3 years ago
5 0

Answer:

DE=6cm

Step-by-step explanation:

Let x=DE, since AB║DE, therefore ∠BAD=∠ADE and ∠ABE=∠BED.        (1)

Also, we are given that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B,

Therefore, ∠EAD=∠DAB and ∠ABE=∠EBD                                             (2)

From (1) and (2), ∠EAD=∠ADE and ∠EBD=∠BED

⇒The ΔADE and ΔEDB then becomes the isosceles triangle with AE=Ed and ED=DB (Sides opposite to equal angles are always equal)

Therefore, AE=DE=DB=x

We are given that the perimeter of ABDE is 30 cm, therefore,

Perimeter of ABDE= sum of all the sides of ABDE

⇒30=AB+BD+DE+AE

⇒30=12+3x

⇒30-12=3x

⇒x=6cm

Therefore, the length of DE= 6cm

You might be interested in
Find the area of the irregular figure.
PilotLPTM [1.2K]

Answer:

Option A. 432\ units^{2}

Step-by-step explanation:

we know that

The area of the irregular figure is equal to the area of two trapezoids

The area of trapezoid is equal to

A=\frac{1}{2}(b1+b2)h

where

b1,b2 are the parallel bases

h is the perpendicular distance between the parallel bases

<u>Find the left trapezoid area</u>

A1=\frac{1}{2}(4+25)(16)=232\ units^{2}

<u>Find the trapezoid area on the right</u>

A2=\frac{1}{2}(25+15)(10)=200\ units^{2}

The area of the irregular figure is

A=A1+A2=232\ units^{2}+200\ units^{2}=432\ units^{2}

6 0
3 years ago
Read 2 more answers
Find the variable 6x-8=34
GenaCL600 [577]

x is the variable

<em>In mathematics, a variable is a symbol; in this case, X.</em>

4 0
3 years ago
Classify each as Linear or Exponential
Marysya12 [62]

Answer:

1. Linear.

2. Exponential.

3. Exponential.

4. Linear.

Step-by-step explanation:            

We have been given some examples of functions and we are asked to classify which of the given functions are linear and exponential.

Since we know that values of a linear function changes at a constant rate, while rate of change of an exponential function is always proportional to the value of function.

Let us see our given function choices one by one.

1. Every year 39 million cars cross the Golden Gate Bridge in San Francisco.

We can see from our function that rate of change for this function is constant as every year same number of cars cross the Golden Gate Bridge, therefore, our function represented by first option is a linear function.

2. Every month a restaurant sells 2% more milkshakes to customers.

We can see from this function that rate of change is not constant as every next month the restaurant sells 2% more milkshakes than last month, therefore, the function represented in 2nd option is exponential function.

3. The number of visitors to the Eiffel Tower in Paris increases by 1.5% each year.  

We can see from this function that rate of change is not constant as every next year the number of visitors is 1.5% more than last year, therefore, the function represented in 3rd option is exponential function.

4. Each week you get $10 and add it to your savings account.

We can see from our function that rate of change for this function is constant as every next week same amount is added to savings account, therefore, our function represented by 4th option is a linear function.

8 0
3 years ago
An art teacher has 24 girls and 40 boys at a soccer camp. The campers will be divided into equal-sized groups. Each group will h
tresset_1 [31]
8 groups is what i suppose
Hope this helps!!! ;-)
5 0
3 years ago
Find h(2/3) if h(x) = 6x <br><br> 2 4 6 8
arlik [135]
H(x) = 6x     

it gives you what x is so plug that in the equation to find it.

h(2/3) = 6(2/3)
h(2/3) = 6 × 2 ÷ 3
h(2/3) = 12 ÷ 3
h(2/3) = 4

so your answer is 4.

hope this helps, God bless!
7 0
3 years ago
Other questions:
  • Margo wants a new carpet and a new wallpaper border for her bedroom. The room is 5.4 meters long and 4 7/8 meters wide. About ho
    8·2 answers
  • How can you use absolute value to represent a negative number in real World situation?
    6·1 answer
  • Pls help ASAP!!!!!!!!!
    10·2 answers
  • Desmond's Surf Shop had the following number of customers on each of the last ten days:
    13·1 answer
  • Zoe paid $ 18.60 $18.60dollar sign, 18, point, 60 in sales tax and tips for her dinner. The sales tax rate is 11 % 11%11, percen
    10·2 answers
  • julie runs 1 and 1/2 miles in 1/3 hour.if julie continues to run at this speed,how many miles will she run per hour
    10·2 answers
  • Ricardo and Brandon ran 1500-meter race. Ricardo finished in 4.89 minutes. Brandon finished in 4.83 minutes. What was the time o
    15·1 answer
  • you have $85 in your bank acount. each week you plan to deposit $8 from your allowance and $15 from ypur paycheck. the equation
    12·2 answers
  • What is cos 60°?
    9·1 answer
  • Consider the diagram.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!