The perimeter of a triangle is 47 miles. The first side is 5 miles less than twice the second and the third is 2 miles more than the first. Find the lengths of each side.
if x is second side,
first is 2x-5
third is 2x-5+2 = 2x-3
so,
2x-5 + x + 2x-3 = 47
5x = 55
x = 11
So, the 3 sides are 17,11,19
To solve this problem, we can use algebraic equations to represent the relationships between the sides of the triangle.
Let's start by assigning variables to represent the lengths of the sides. Let the second side be x miles.
According to the problem, the first side is 5 miles less than twice the second side. This can be expressed as:
First side = 2x - 5
The third side is 2 miles more than the first side. So, we can write the length of the third side as:
Third side = (2x - 5) + 2
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is 47 miles. So we can set up the equation:
(First side) + (Second side) + (Third side) = Perimeter
(2x - 5) + x + ((2x - 5) + 2) = 47
Now, we can solve this equation to find the value of x, which represents the length of the second side.