the 3 sides of a triangle have lengths of (x+7) inches, (5x+6) inches, and (5x-3) inches. What is the length of the shortest side if the perimeter of the triangle is 43 inches
x + 7 + 5x + 6 + 5x - 3 = 43
11x + 10 = 43
11x = 33
x = 3 inches
10 + 21 + 12
To find the length of the shortest side of the triangle, we need to determine the values of x that make the sum of the three sides equal to the perimeter of 43 inches.
The perimeter of a triangle is the sum of all three sides. In this case, the sum of the three sides is given by:
(x+7) + (5x+6) + (5x-3) = 43
To solve this equation, we need to combine like terms and then solve for x:
11x + 10 = 43
Subtracting 10 from both sides:
11x = 33
Dividing both sides by 11:
x = 3
Now that we have determined the value of x, we can substitute it into any of the three side lengths to find the lengths of the individual sides.
For example, substituting x = 3 into (x+7) inches:
(3+7) = 10 inches
The length of the shortest side is 10 inches.