I need help please on this...?

Question

The perimeter of a triangle is 56. The longest side measures 4 in. less than the sum of the two other sides. Three times the shortest side is 4 in more than the longest side. find the lenghts of the three sides.

I believe I am suppose to go :
L= A+B - 4
3B= L+4
A= ?

Then I don't know what steps to do next. Could you help me through this. Thanks. My husband is of no help right now.

Answer 1

You're on the right track!

Rewrite the second equation as: 3B - 4 = L

Now, substitute for L back into the first equation:
3B - 4 = A + B - 4
3B = A + B
2B = A

Now we know A + B + L = 56, so:
(2B) + B + (3B - 4) = 56
6B = 60
B = 10

So:
2B = A
20 = A

L = A + B - 4
L = 20 + 10 - 4
L = 26

So the lengths are 10, 20, and 26, which add up to 56.

Answer 2

Start with the shortest side. Call it S. Call the middle side M. Call the long side L.

Then : 3S - 4 = L (more usable than 3S = L + 4)
S + M - 4 = L
S + M + L = 56

3S - 4 = S + M - 4 (both = to L)

2S = M (subtract S, add 4 to both sides)
3S + L = 56 (substitute 2S for M in last equation)
L = 56 - 3S
3S - 4 = 56 - 3S (both = to L)
6S = 60 (add 3S and add 4 to both sides)

S = 10 (divide both by 6)

M = 2S = 2 x 10 = 20

L = S + M - 4 = 10 + 20 - 4 = 26

Check : S + M + L = 56

10 + 20 + 26 = 56

Answer 3

L = A+B - 4
3B = L+4
the third equation to figure out the 3 variables is
A+B+L = 56

There are many ways to proceed from here. One is:
L = 3B - 4 (from your 2nd equation)
3B - 4 = A+B - 4 (from your 1st equation)
3B = A + B
2B = A

2B + B + L = 56 (from the 3rd equation)
2B + B + (3B - 4) = 56
6B - 4 = 56
6B = 60
B = 10

A = 20 (because 2B=A)
L = 26 (because A+B+L=56)

Answer 4

3 sides, 3 variables, need 3 equations. 3rd one is perimeter = A + B + L = 56, then start substituting:

L = A + B - 4
L = (56 - L) - 4
2L = 52
L = 26
3B = 26 + 4
3B = 30
B = 10
A + 10 + 26 = 56
A = 20

Answer 5

Let's set up your equations.
First of all, A+B+L=56.
Then
L = A+B+4.
Why? L is 4 in. LESS than the sum of the other
2 sides, so you have to add 4 to the sum to get L.
Finally,
3B = L-4. (Same sort of reasoning)
Now let's solve the system:
3B+4 = A+B+4 (plugging into the second equation)
So A = 2B.
Thus 2B +B + 3B-4 = 56.
6B=60
B=10
A = 20
L = 26.
Let's check our answer:
L = 26 =10+20-4,
and
30 = 26+4.
Hope that helps!

Answer 6

You have three variables and two equations. The third equation you're looking for is:

A + B + L = 56

Now, you can solve for three variables.

A + B + L = 56
A + B - L = 4
-------------------
2A + 2B = 60

A + B = 30

A = 30 - B

L = (30 - B) + B - 4
L = 26

3B = 26 + 4 = 30
B = 10
A = 20

Done!

Answer 7

L=A+B-4

L+4=A+B

but question says; 3B=L+4,

so A+B=3B

therfore; A=3B-B

A=2B

hope it helps..