Given Perimeter of triangle is 26 inches.
Side A is 3 inches longer than B.
Side C is 1 inch shorter than twice side B
A+B+C = 26
(B+3)+B+(2B-1) = 26
Now you find B, and thus A and C.
To proceed, let's denote the lengths of the sides of the triangle as follows:
Side A: x inches
Side B: y inches
Side C: z inches
We are given three pieces of information about the sides:
1) The perimeter of the triangle is 26 inches.
Perimeter = A + B + C
So, we can write the equation: x + y + z = 26
2) Side A is 3 inches longer than Side B.
This can be represented as: x = y + 3
3) Side C is 1 inch shorter than twice Side B.
This can be represented as: z = 2y - 1
Now, we have a system of equations:
x + y + z = 26
x = y + 3
z = 2y - 1
We can solve this system of equations to find the values of x, y, and z.
To eliminate x from the equations, we can substitute the value of x from the second equation into the first equation:
(y + 3) + y + z = 26
Simplifying this equation, we get:
2y + z = 23 -- Equation (4)
Now, we need to substitute the value of z from the third equation into Equation (4):
2y + (2y - 1) = 23
Simplifying further, we get:
4y - 1 = 23
4y = 24
y = 6
Now, substitute the value of y back into Equation (4):
2(6) + z = 23
12 + z = 23
z = 11
Finally, substitute the values of y and z into the equation x = y + 3:
x = 6 + 3
x = 9
Therefore, the lengths of the sides of the triangle are:
Side A: 9 inches
Side B: 6 inches
Side C: 11 inches