In triangle ABC, if line BC is one inch longer than line AB, line AC is 10 inches shorter than the sum of line BC and line AB , and the perimeter of triangle ABC is 72 inches, find the length of line BC?
To find the length of line BC, we can use algebraic equations based on the given information. Let's denote the length of AB as x.
Since line BC is one inch longer than line AB, its length can be expressed as x + 1.
Given that line AC is 10 inches shorter than the sum of line BC and line AB, we have the equation AC = (AB + BC) - 10. Substituting the values of AB and BC, we get AC = (x + x + 1) - 10 = 2x - 9.
The perimeter of triangle ABC is the sum of the lengths of all three sides, which is equal to 72 inches. Therefore, we have the equation AB + BC + AC = 72. Substituting the values, we get x + (x + 1) + (2x - 9) = 72.
Simplifying the equation, we have 4x - 8 = 72.
Adding 8 to both sides, we get 4x = 80.
Dividing both sides by 4, we find x = 20.
Now that we have the value of x, we can substitute it back into the equation for BC: BC = x + 1 = 20 + 1 = 21.
Therefore, the length of line BC is 21 inches.