the perimeter of a triangle is 51 centimeters, the longest side is 1 centimeter less than the sum of the other two sides. twice the shortest is 11 centimeters less than the longest side. find the lengths of each side of the triangle.

Question

the perimeter of a triangle is 51 centimeters, the longest side is 1 centimeter less than the sum of the other two sides. twice the shortest is 11 centimeters less than the longest side. find the lengths of each side of the triangle.

Answer 1

L=S1+S2-1

2*S1+11=L
L+S1+S2=51

rearranging these
S1+S2-L=1
2S1 -L=-11
S2+S2+L=51

add the two last equations
2S1+S2=40
subtract the first from the second
S1-S2=-12
add these two equations
3S1=28
S1=7

can you take if from here?

Answer 2

... add the two last eq.

3S1+S2=28
...
4S1=28

Answer 3

Thanks. I typoed and did not catch it.

Answer 4

To solve this problem, let's start by assuming that the lengths of the three sides of the triangle are represented by x, y, and z, with z being the longest side.

We are given two pieces of information:

1. The perimeter of the triangle is 51 centimeters. Perimeter is the sum of all three sides of the triangle. So, we can write the equation:
x + y + z = 51

2. The longest side is 1 centimeter less than the sum of the other two sides. This can be expressed as:
z = x + y - 1

Now, we can use the second piece of information to substitute the value of z in the first equation to express it only in terms of x and y:
x + y + (x + y - 1) = 51
2x + 2y - 1 = 51
2x + 2y = 52
x + y = 26

We have now reduced the problem to solving a system of linear equations with two variables, x and y. Let's solve this system using the method of substitution.

From the equation x + y = 26, we can express x in terms of y:
x = 26 - y

Substituting this value of x into the equation z = x + y - 1:
z = (26 - y) + y - 1
z = 25

So, we have x = 26 - y and z = 25.

Now, we can substitute these values into the initial equation to find the lengths of each side. Let's substitute x = 26 - y, y = y, and z = 25 into the equation x + y + z = 51:
(26 - y) + y + 25 = 51
51 - y = 51
y = 0

Now that we have the value of y, we can substitute it back into the equation x = 26 - y:
x = 26 - 0
x = 26

Finally, we can find the values of x, y, and z. The lengths of each side of the triangle are:
x = 26 centimeters
y = 0 centimeters
z = 25 centimeters