Question

use the image to answer the question. image long description if quadrilateral rstu is a parallelogram, what are the lengths of the diagonals of the figure? (1 point) diagonal rt is equal to and diagonal su is equal to

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So $RV = VT$ and $SV=VU$.
We have the equations: $3m + 2=4m - 3$ and $2n+2=8 + n$.

Step2: Solve for $m$

Solve the equation $3m + 2=4m - 3$ for $m$.
Subtract $3m$ from both sides: $2=m - 3$.
Add 3 to both sides: $m=5$.

Step3: Solve for $n$

Solve the equation $2n+2=8 + n$ for $n$.
Subtract $n$ from both sides: $n+2 = 8$.
Subtract 2 from both sides: $n = 6$.

Step4: Calculate length of diagonal $RT$

$RT=RV + VT$. Since $RV=3m + 2$ and $m = 5$, then $RV=3\times5+2=15 + 2=17$ and $RT=2RV=34$.

Step5: Calculate length of diagonal $SU$

$SU=SV+VU$. Since $SV=2n + 2$ and $n = 6$, then $SV=2\times6+2=12 + 2=14$ and $SU=2SV=28$.

Answer:

Diagonal $RT$ is equal to $34$ and diagonal $SU$ is equal to $28$.