Question

the perimeter of the rectangle below is 64 units. find the length of side $overline{bc}$.
write your answer without variables.
$4x - 3$
$3x$
$bc = \square$

Explanation:

Step1: Recall rectangle perimeter formula

Perimeter $P = 2(\text{length} + \text{width})$
Substitute values: $64 = 2(3x + 4x - 3)$

Step2: Simplify the equation

First simplify inside parentheses: $64 = 2(7x - 3)$
Divide both sides by 2: $32 = 7x - 3$

Step3: Solve for $x$

Add 3 to both sides: $35 = 7x$
Divide by 7: $x = 5$

Step4: Calculate length of $\overline{BC}$

$\overline{BC} = 4x - 3$, substitute $x=5$: $\overline{BC} = 4(5) - 3$

Answer:

17