The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side if the perimeter is not more than 120 inches.
5x+12x+13x <= 120
30x <= 120
x <= 4
so, the shortest side can be no more than 20.
To find the length of the shortest side of the triangle, we need to determine the actual lengths of the sides. We are given the ratio of the side lengths as 5:12:13.
Let's assume the common ratio of the sides is x. Therefore, we can express the lengths of the sides as 5x, 12x, and 13x.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as not more than 120 inches. So, we can write the following inequality based on the lengths of the sides:
5x + 12x + 13x ≤ 120
Simplifying the equation, we have:
30x ≤ 120
Dividing both sides by 30 to solve for x:
x ≤ 4
Since x represents the common ratio of the side lengths, it must be a positive value. Therefore, x can take any value less than or equal to 4.
To find the length of the shortest side, we substitute the maximum value of x (which is 4) into our expression for the shortest side (5x):
Shortest side = 5 * 4 = 20 inches
Thus, the length of the shortest side of the triangle is 20 inches when the perimeter is not more than 120 inches.