the length of tr is 17 units. what are the lengths of sv and qt? sv = units qt = units

Explanation:

Step1: Use property of rhombus diagonals

In a rhombus, diagonals are perpendicular bisectors of each other. So, $TR = RV$ and $QT=QS$. Given $TR = 17$ units, then $RV=17$ units. Also, $3x + 2=17$.

Step2: Solve for $x$

Solve the equation $3x+2 = 17$. Subtract 2 from both sides: $3x=17 - 2=15$. Then divide both sides by 3: $x=\frac{15}{3}=5$.

Step3: Find length of $SV$

The length of $SV$ is composed of two equal - length segments $TR$ and $RV$. So $SV=2\times17 = 34$ units.

Step4: Find length of $QT$

Substitute $x = 5$ into the expression for $QT$ which is $4x + 1$. So $QT=4\times5+1=20 + 1=21$ units.

Answer:

$SV = 34$ units $QT = 21$ units