Question

find fg in rectangle defg.
fg =
submit

Explanation:

Step1: Set equal opposite sides

In a rectangle, opposite sides are equal, so $5v-52 = v$.

Step2: Solve for $v$

Subtract $v$ from both sides: $4v-52=0$.
Add 52 to both sides: $4v=52$.
Divide by 4: $v=\frac{52}{4}=13$.

Step3: Calculate length of $FG$

Substitute $v=13$ into $FG=2v-21$:
$FG=2(13)-21=26-21=5$.
Wait, correction: Opposite sides are $FG$ and $ED$, $FE$ and $GD$. So $FE=GD$: $5v-52 = v$, solve to get $v=13$. Then $FG=2v-21=2*13-21=26-21=5$. No, wait, no: $GD = v$, $FE=5v-52$, so $5v-52 = v$ gives $4v=52$, $v=13$. Then $FG=2v-21=2*13-21=5$. Wait, no, wait, rectangle has opposite sides equal: $FG = ED$, $FE=GD$. So $FE=5v-52$, $GD=v$, so $5v-52 = v$, $v=13$. Then $FG=2v-21=2*13-21=5$. Yes, that's correct.

Wait, correction, final answer is 5.

Step1: Equate opposite rectangle sides

In rectangles, opposite sides are equal: $5v-52 = v$

Step2: Solve for variable $v$

$5v - v = 52 \implies 4v=52 \implies v=\frac{52}{4}=13$

Step3: Compute length of $FG$

Substitute $v=13$ into $FG=2v-21$:
$FG=2(13)-21=26-21=5$

Answer:

19