A triangle has a perimeter of 35inches. The length of side a of the triangle is twice the length of side b. Side c is 5inches longer than side a. What is the length of each side of the triangle?
b + 2b + 2b + 5 = 35
5b + 5 = 35
5b = 30
b = 6
To find the length of each side of the triangle, we can set up equations based on the given information and solve them.
Let's denote the length of side a as "x". Since side a is twice the length of side b, we can express side b as "x/2".
As stated, side c is 5 inches longer than side a. So, side c can be expressed as "x + 5".
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is 35 inches. So, we can set up the equation:
x + (x/2) + (x + 5) = 35
To solve this equation, we need to combine like terms:
(2/2)x + (1/2)x + 5 = 35
Simplifying further:
(3/2)x + 5 = 35
Next, we can isolate the variable by subtracting 5 from both sides:
(3/2)x = 30
To eliminate the coefficient of (3/2), we can multiply both sides by its reciprocal, which is 2/3:
((3/2)x)(2/3) = 30(2/3)
Simplifying further:
x = 20
Therefore, the length of side a is 20 inches.
To find the length of side b, we use the given information that side a is twice the length of side b:
b = (1/2)x
Substituting the value of x:
b = (1/2)(20)
b = 10
Therefore, the length of side b is 10 inches.
To find the length of side c, we use the information that side c is 5 inches longer than side a:
c = x + 5
Substituting the value of x:
c = 20 + 5
c = 25
Therefore, the length of side c is 25 inches.
In conclusion, the length of each side of the triangle is:
Side a: 20 inches
Side b: 10 inches
Side c: 25 inches