The perimeter of a triangle is 26 c,. Side a of the triangle is 3 cm longer than side b. Side c is 1 cm shorter than twice side b. Find the length of each side.
a+b+c=26
a=b+3
c=2b-1
can you take if from here?
a = b+3
c = 2b - 1
a + b + c = 26
b+3 + b + 2b-1 = 26
b = 8
a = 11
b = 8
c = 15
Do these answers satisfy the conditions stated in your problem?
To find the length of each side of the triangle, let's denote side a as A, side b as B, and side c as C.
According to the given information, the perimeter of the triangle is 26 cm, which means the sum of all three sides is 26 cm. We can express this information as an equation:
A + B + C = 26
The problem also states that side A is 3 cm longer than side B, so we can write:
A = B + 3
Additionally, side C is 1 cm shorter than twice side B, so we can write:
C = 2B - 1
Now we have a system of two equations that we can solve simultaneously to find the values of A, B, and C.
Substituting the expressions for A and C into the first equation, we get:
(B + 3) + B + (2B - 1) = 26
Simplifying the equation:
4B + 2 = 26
Subtracting 2 from both sides:
4B = 24
Dividing both sides by 4:
B = 6
Now that we have the value of side B, we can substitute it back into the equations to find the values of A and C.
Using the expression for A:
A = B + 3 = 6 + 3 = 9
Using the expression for C:
C = 2B - 1 = 2(6) - 1 = 11
Therefore, the lengths of the sides of the triangle are:
A = 9 cm
B = 6 cm
C = 11 cm