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
sasho [114]
3 years ago
5

If DE = 37 cm and EF = 16 cm, then what are the possible lengths for DF so that DE,EF, and DF can form a triangle? Explain your

reasoning.
Mathematics
2 answers:
Brut [27]3 years ago
7 0

Answer:

The length of DF must be between 21 and 53.

Step-by-step explanation:

In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.

EF + DF > DE

16 + DF > 37

DF > 21

Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.

DE + EF > DF

37 + 16 > DF

53 > DF

With these two in mind, we know that DF must be between 21 and 53

tigry1 [53]3 years ago
3 0

Answer: 21 < DF < 53 ; Triangle Inequality Theorem

<u>Step-by-step explanation:</u>

The Triangle Inequality Theorem states that the sum of any two sides is greater than the sum of the third side.

DE + EF > DF          EF + DF > DE                 DE + DF > EF

37 + 16 > DF           16 + DF > 37                  37 + DF > 16

       53 > DF                   DF > 21                           DF > -21


Now let's put together the answers.  Note that DF > -21 is irrelevant since all lengths must be greater than 0.

53 > DF  and DF > 21  means that DF is between 53 and 21

----->    21 < DF < 53


You might be interested in
Which of the following units for mass is an SI unit?
s2008m [1.1K]
Kilogram is an SI unit for mass.
Ounce and pound refer to American system for measuring things, and decakilogram is not the "basic" unit, but kilogram is.
5 0
2 years ago
Read 2 more answers
SOMEONE HELP ME PLZ ASAP!!!!​
Elanso [62]

A=22cm

B=21cm

C=23cm

Good luck

4 0
3 years ago
Help me this is the last question i just need to know what to use to solve the problem
Genrish500 [490]

Answer:

Not even one day

Step-by-step explanation:

I mean if it uses 4 bags a day  . . .

2/5's wont last long at all

8 0
3 years ago
A polynomial function has roots –5 and 1. Which of the following could represent this function? f(x) = (x + 5)(x + 1) f(x) = (x
Dimas [21]

f(x) = (x + 5)(x - 1)

using the ' factor theorem '

given x = a is the root of a polynomial then (x - a ) is a factor

here roots are x = - 5 and x = 1 hence factors are (x + 5) and (x - 1)

the polynomial is the product of the factors

f(x) = (x + 5)(x - 1)


3 0
3 years ago
Read 2 more answers
Find x, y, and z:<br><br><br><br> x = <br><br> y = <br><br> z =
Ivanshal [37]

Answer:

x=81 degrees

y=132 degrees

z=60 degrees

5 0
3 years ago
Read 2 more answers
Other questions:
  • Plz help. A tram moved upward 3 meters per second for 24 seconds. What was the total change in the tram's elevation?
    8·1 answer
  • How many planets are there
    11·2 answers
  • which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5-2m6+5m2n4-m3n3+n6-4
    12·1 answer
  • sonja and jake just got married. they received $4,500 in gift money and deposited it into a savings account that pays 1.85% simp
    6·1 answer
  • Which angle is an x-intercept for the function y = cos(1/2x)
    9·2 answers
  • I will mark who ever gets it correct the brainiest.<br> Help Asap. See image below.
    12·1 answer
  • How do I Convert Mixed Numbers to Improper Fractions
    5·2 answers
  • half of an integer exceeds one _ third of the next integer by unity .Find the integer. please ask fast​
    8·1 answer
  • The set of integers from -3 to 3
    10·1 answer
  • LeRoy cut a length of string into 30
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!