A triangle has a perimeter of 8x + 7. The first side of the triangle has a length of 4x, and the second side has a length of 2x − 3. What is the length of the third side of the triangle?
To find the length of the third side, we need to subtract the first two side lengths from the perimeter and simplify:
Perimeter = 8x + 7
First side = 4x
Second side = 2x - 3
Third side = Perimeter - First side - Second side
Third side = (8x + 7) - (4x) - (2x - 3)
Third side = 8x + 7 - 4x - 2x + 3
Third side = 2x + 10
Therefore, the length of the third side is 2x + 10.
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle, which states that the perimeter is the sum of the lengths of all three sides.
Given that the perimeter is 8x + 7, the first side has a length of 4x, and the second side has a length of 2x - 3, we can set up the equation:
Perimeter = First side + Second side + Third side
8x + 7 = 4x + (2x - 3) + Third side
Simplifying the equation:
8x + 7 = 6x - 3 + Third side
To isolate the Third side, we first bring like terms together:
8x + 7 = 6x - 3 + Third side
Next, we combine like terms on the right side:
8x + 7 = 6x - 3 + Third side
8x + 7 = 6x - 3 + Third side
Simplifying further:
8x + 7 = 6x - 3 + Third side
8x + 7 - 6x + 3 = Third side
Simplifying again:
8x - 6x + 7 + 3 = Third side
2x + 10 = Third side
Therefore, the length of the third side of the triangle is 2x + 10.