Examine rectangle JKLI , shown below. If JN=x+3 and JL=3x+1 determine which of the following values are correct.Select al/ that apply. NL=4 D JN=5 NM=8 KM=10 JL=16

To solve this problem, we need to use the properties of a rectangle. In a rectangle, opposite sides are equal in length, and the diagonals are also equal in length.Given:- \(JN = x + 3\)- \(JL = 3x + 1\)Since \(JKLM\) is a rectangle, we know that \(JL = KM\) and \(JN = LM\).Now let's examine the given options one by one:1. \(NL = 4\)Since \(NL\) is not a side of the rectangle and we don't have enough information about it, we cannot determine its length without additional information. Therefore, we cannot confirm this statement.2. \(JN = 5\)If \(JN = 5\), then we can set \(x + 3 = 5\) and solve for \(x\):\(x + 3 = 5\)\(x = 5 - 3\)\(x = 2\)Now we can check if \(JL = 3x + 1\) equals 16 when \(x = 2\):\(JL = 3(2) + 1\)\(JL = 6 + 1\)\(JL = 7\)Since \(JL\) does not equal 16 when \(x = 2\), the value \(JN = 5\) does not satisfy the condition \(JL = 3x + 1\). Therefore, this statement is incorrect.3. \(NM = 8\)Since \(NM\) is not a side of the rectangle and we don't have enough information about it, we cannot determine its length without additional information. Therefore, we cannot confirm this statement.4. \(KM = 10\)If \(KM = 10\), then \(JL = 10\) as well because they are opposite sides of the rectangle. However, we have \(JL = 3x + 1\), so we can set \(3x + 1 = 10\) and solve for \(x\):\(3x + 1 = 10\)\(3x = 10 - 1\)\(3x = 9\)\(x = 3\)Now we can check if \(JN = x + 3\) equals 5 when \(x = 3\):\(JN = 3 + 3\)\(JN = 6\)Since \(JN\) does not equal 5 when \(x = 3\), the value \(KM = 10\) does not satisfy the condition \(JN = x + 3\). Therefore, this statement is incorrect.5. \(JL = 16\)If \(JL = 16\), then we can set \(3x + 1 = 16\) and solve for \(x\):\(3x + 1 = 16\)\(3x = 16 - 1\)\(3x = 15\)\(x = 5\)Now we can check if \(JN = x + 3\) equals 5 when \(x = 5\):\(JN = 5 + 3\)\(JN = 8\)Since \(JN\) does not equal 5 when \(x = 5\), the value \(JL = 16\) does not satisfy the condition \(JN = x + 3\). Therefore, this statement is incorrect.Based on the analysis above, none of the given values are correct.