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?
2. marie is centering a tapestry on her living room wall. as shown in the figure below, the rectangular wall is 36 feet in length, and the tapestry is 4 feet in height and 8 feet in length. the right edge of the tapestry will be x feet from the right edge of the wall, and the left edge of the tapestry will also be x feet from the left edge of the wall. what is the value of x in feet?

Explanation:

Step1: Set up the equation

The sum of the two \(x\) - lengths and the length of the tapestry equals the length of the wall. So, \(2x+8 = 36\).

Step2: Solve the equation for \(x\)

Subtract \(8\) from both sides of the equation: \(2x=36 - 8\). Then \(2x = 28\). Divide both sides by \(2\): \(x=\frac{28}{2}=14\).

Answer:

\(x = 14\)