I need help with this algebra story problem. Can you help me please?

Question

The perimeter of a triangle is 51 cm. The measure of the smallest side is 4 less than the middle side. The measure of the longest side is equal to one less than the sum of the other sides. Find the lengths of the sides.


THANK YOU SO MUCH FOR YOUR HELP!

Answer 1

Since you're given that the perimeter is 51 cm and with all the others parameters we can let x = to the shortest side, y = middle side, and z = to the longest side of you're triangle and in equations we have:

x + y + z = 51
x = y - 4
z = (x + y) -1

First we know that
x + y + z = 51 &
z = (x + y) -1 ---> (x + y) = z + 1

so; x + y + z = 51
(z + 1) + z = 51
2z = 50
z = 25

Now we have z = 25 & x = y - 4
z = (x+y) -1
25 = ((y-4)+y) -1
25 = 2y - 5
2y = 30
y = 15

and for the third side:
x + y + z = 51
x + 15 + 25 = 51
x + 40 = 51
x = 51 - 40
x = 11

So our three sides of the triangle are 11cm, 15cm, and 25 cm.

Answer 2

Triangles have 3 sides.
In this case, call the sides s, m, L for small, middle, long.

Make the sentences into equations.
The measure of the smallest side is 4 less than the middle side.
s = m-4
The longest side equals one less than the sum of the other sides.
L = s + m - 1 Substitute m-4 for s. We found that out in the first equation.
L = (m-4) + m - 1
L = 2m - 5

Now we have all three sides in terms of L. We know that adding all the sides together makes 51 cm.
small + middle + long = 51 cm
(m-5) + m + (2m-4) = 51 cm
4m - 9 = 51 cm
4m = 60 cm
m = 15 cm = medium side
s = m-4 = 15-4 = 11 cm = smallest side
L = m + s - 1 = 15 + 11 - 1 = 25 cm = longest side


Check:
15 + 11 + 25 = 51 cm Correct!

Answer 3

Let's call the shortest side "a", the middle side "b", and the longest side "c". Here's what you know from the information given:

a+b+c=51
a=b-4
c=a+b-1

Now the key is to figure out how to use these equations in such a way that you only have one variable to solve for and then you can figure out the other two. You can do this by expressing each variable in terms of b. Obviously, b=b. But you also know that a=b-4. Since you know that, you can also say that c=(b-4)+b-1, which simplifies to c=2b-5.

Now, plug all three of those into your first equation.
a+b+c=51
(b-4) + b + (2b-5) = 51
b-4+b+2b-5=51
b+b+2b=60
4b=60
b=15

Now that you know the value of b, you can easily solve for the other two.

a=b-4
a=15-4
a=11

c=a+b-1
c=11+15-1
c=25

So, a=11, b=15, and c=25. If you go back and double-check to make sure these work with the information given in the problem, you can see that they do.

Answer 4

x=The measure of the smallest side.
y=The measure of the middle side.
z=The measure of the longest side.

x+y+z=51
x=y-4
z=x+y-1

y-4+y+x+y-1=51
3y-4+y-4-1=51
4y=51+9
y=60/4
y=15
x=15-4=11
z=11+15-1
z=25

Answer 5

Side A = A
Side B = A-4
Side C = A + A-4 -1

A + A-4 + A + A-4 -1 = 51
4A = 60
A = 15
Side B = 11
Side C = 25

Answer 6

11, 15, 25