Question

1. a triangle abc has a perimeter of 22 centimeters with side that is 7 centimeters long. the length of the remaining two sides have a ratio of 2:3. what is the length, in centimeters, of the shortest side of the triangle?

Explanation:

Step1: Calculate the sum of the remaining two sides

The perimeter of the triangle is \(22\) cm and one side is \(7\) cm. So the sum of the remaining two sides is \(22 - 7=15\) cm.

Step2: Use the ratio to find the lengths of the sides

Let the lengths of the two sides be \(2x\) and \(3x\). Then \(2x + 3x=15\), which simplifies to \(5x = 15\). Solving for \(x\), we get \(x = 3\).
The lengths of the two sides are \(2x=2\times3 = 6\) cm and \(3x=3\times3 = 9\) cm.
Comparing the three sides (\(6\), \(7\), \(9\)), the shortest side is \(6\) cm.

Answer:

\(6\)