Question

The perimeter of a triangle is 45 centimeters. The longest side is 5 centimeter(s) less than the sum of the other two sides. Twice the shortest side is 4 centimeters less than the longest side.
Find the lengths of each side of the triangle.
The length from the shortest to longest are_, _, and _ centimeters?

Answer 1

The information you're given allows you to set up three equations in three unknowns. Name the sides as:

l = longest
s = shortest
a = remaining side

The perimeter is 45, which is the sum of the lengths of the sides, so\[l+s+a=45\]is one equation. You're told that the longest side is 5 LESS than the SUM of the other two sides, so\[l=a+s-5\]and finally, TWICE the shortest side equals 4 LESS than the longest, namely,\[2s=l-4\]

Answer 2

You have three linear equations in three unknowns, so you can solve the system exactly.

Answer 3

Lol. Ok, so what;s the answers though?

Answer 4

i like the way you explain it though...

Answer 5

Well, you have to do some substituting. Take any one of you equations to begin with. Use the second to plug into the third to eliminate for l. So,\[2s=(a+s-5)-4=a+s-9 \rightarrow a=s+9\]

Answer 6

Let me sort it.

Answer 7

.......

Answer 8

It's fast to do on paper but a pain to do online.

Answer 9

tell me about it...

Answer 10

If you sub. the equation for l (second one) into the first, you should get\[(a+s-5)+s+a=45 \rightarrow s+a=20\]

Answer 11

If you sub the same second equation for l into the third, you get\[2s=(a+s-5)-4 \rightarrow a-s=9\] (forget the equation I solved at the very beginning, I stuffed the sign).

Answer 12

You now have \[a+s=20\]and\[a-s=9\]

Answer 13

If a=9+s from the second equation here, then putting it into the first, you get\[(9+s)+s=20 \rightarrow 2s=11 \rightarrow s=\frac{11}{2}\]

Answer 14

lol..this is a monster!

Answer 15

Which means, from any of the two equations involving a and s above, for a,\[a=9+s=9+\frac{11}{2}=\frac{29}{2}\]

Answer 16

Now from your perimeter equation, you can solve for l:\[l=45-a-s=45-\frac{29}{2}-\frac{11}{2}=25\]

Answer 17

You're done.

Answer 18

Well, I am...

Answer 19

so it's how many centimeters each?

Answer 20

Just look through -

l = 25 cm
s = 5.5 cm
a = 14.5 cm

Answer 21

crap

Answer 22

crap what?

Answer 23

The correct answers were 8,17, and 20! :(

Answer 24

Now it reformulates a new, but similar problem for me to solve.

Answer 25

Now it's......

Answer 26

The perimeter of a triangle is 45 centimeters. The longest side is 5 centimeter(s) less than the sum of the other two sides. Twice the shortest side is 4 centimeters less than the longest side.
Find the lengths of each side of the triangle.
The length from the shortest to longest are_, _, and _ centimeters?

Answer 27

Yes a mistake was made. You need to check everything once it's solved but putting it back into the equations.

Answer 28

its the same one!
never had that happen before.

Answer 29

so what would be the "mistake free" answer? :)

Answer 30

Well, if it's the same question, you already have the answers - you just posted them!

Answer 31

LOL......DUH!

Answer 32

I didn't even think of that.

Answer 33

Sigh......long day.

Answer 34

Want a shot at another?

Answer 35

Depends, if you give me back my fan point ;)

Answer 36

Fair enough!

Answer 37

Do you have the question?

Answer 38

Yeah, it's a beast....
one sec.....

Answer 39

In a certain year out of pocket expenses for an elderly person in poor health were 3353 more than for an elderly person in good health. Combined out of pocket expenses for one person in poor health and one person in good health was 6677 find the our of pocket expenses for each type of person.
Out of pocket expenses for a person in poor health was....
Out of pocket expenses for a person in good health was....

Answer 40

phew!

Answer 41

Do you just want the answer?

Answer 42

Did you take my point off again? lol

Answer 43

lol...me? Nooooooo! Why would you ask that?! ;)

Answer 44

poor health person = 5015
good health person = 1662

Answer 45

Yes.....I was holding it hostage until you returned. It's back.

Answer 46

Ok......now enlighten me how you got it so darn fast! I have a friend on here that is taking the same class and I want to help her too.

Answer 47

She is Kelley29 I think..

Answer 48

poor health out-of-costs = p
good health out-of-costs = g

Information says

p = 3353 + g
p + g = 6677

Solve the two. First is p=3353 + g so sub. into second to get rid of p:

(3353 + g) = 6677

Answer 49

.............

Answer 50

g=6677-3353=1662

Answer 51

p=3353+ g = 3353 + 1662 = 5015

Answer 52

Ok what her numbers are poor health=3334, good health=6596

Answer 53

she just gave me that, and I have no idea what that formula is you just gave me.....unfortunately.
I will tell her to give you a POINT!

Answer 54

you're a star

Answer 55

Whats tha t mean?

Answer 56

It just means I appreciate your offer to get your friend to give me a point.

Answer 57

Lol, i'ts the least I can do!

Answer 58

SO what is it?

Answer 59

what is what?

Answer 60

her answer! lol

Answer 61

U need more info?

Answer 62

I don't have her question - what's her login name?

Answer 63

Just give me a second, I'm just helping someone else too.

Answer 64

Same questions!
Hers is Kelley29

Answer 65

Ok n/m some dude just got it for her.

Answer 66

But...we have more. At least a coupla more.

Answer 67

Kelly29 is being helped by blexting.

Answer 68

He/she does a good job.

Answer 69

Ok, well I have more...

Answer 70

Translate to a system of equations, but do not solve.
An non toxic floor wax can be made from lemon juice and food grade linseed oil.
The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 42 ounces of floor wax?
Let x represent the number of ounces of lemon juice and y the number of ounces of linseed oil.
Complete the system of equations.
y=
x+y=

Answer 71

It's absolutely ridiculous!

Answer 72

...........

Answer 73

y=2x

x+y =42
------------------------------------------------------
You're told you need 2 times as much x as y (2 times as much lemon juice as linseed oil).

You also know that the total weight, x + y, should be 42 oz.

Answer 74

ANd AGAIN........you got it right!

Answer 75

last one here for the night.....i promise.........

Answer 76

If a plane can travel 480 miles per hour with the wind, and 380 miles per hour against the wind, find the speed of the plan without a wind and the speed of the wind.
The speed of the plan in still air is _miles per hour.

Answer 77

It's 430 miles per hour

Answer 78

Ok........the speed of the WIND is?

Answer 79

50, sorry, forgot

Answer 80

50mph?

Answer 81

Ok, can you PLEASE help my friend now.....you rock, and these other guys suck apparently! I will tell her to rock your points! :,)

Answer 82

Thank you very much by the way......I really do appreciate your help.

Answer 83

Thanks for the praise. I'll see what I can do. I promised someone else I'd help him and he's been waiting. If kelley29 is still around when I'm done, I'll help.

Answer 84

I understand. You're the best! I hope to see you on here for the next 4 weeks or so.