Question

The longest side of a triangle is 3 times the shortest side, and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

(a) 10 cm
(b) 11 cm
(c) 12 cm
(d) 13 cm

Answer 1

The minimum length of the shortest side of the triangle is 9 cm.

Step-by-step explanation:

To find the minimum length of the shortest side of the triangle, we need to set up equations based on the given information. Let's say the shortest side is x cm. According to the problem, the longest side is 3 times the shortest side, so the longest side is 3x cm. And the third side is 2 cm shorter than the longest side, so it is (3x - 2) cm. The perimeter of the triangle is at least 61 cm, which can be expressed as:

x + 3x + (3x - 2) ≥ 61

Simplifying this equation, we get:

7x - 2 ≥ 61

Adding 2 to both sides, we get:

7x ≥ 63

Dividing both sides by 7, we get:

x ≥ 9

Therefore, the minimum length of the shortest side is 9 cm.