Question

quadrilateral rstu is a rhombus. what is rs? rs =

Explanation:

Step1: Recall rhombus property

In a rhombus, all sides are equal. So, $RS = RU$. Set up the equation $20t - 86=2t + 4$.

Step2: Solve for t

Subtract $2t$ from both sides: $20t-2t - 86=2t-2t + 4$, which simplifies to $18t-86 = 4$. Then add 86 to both sides: $18t-86 + 86=4 + 86$, getting $18t=90$. Divide both sides by 18: $t=\frac{90}{18}=5$.

Step3: Find length of RS

Substitute $t = 5$ into the expression for $RS$ (we can use either $RS=20t - 86$ or $RS=2t + 4$). Using $RS=2t + 4$, we have $RS=2\times5+4=10 + 4=14$.

Answer:

14