Question

find cd and bc in parallelogram bcde. cd = bc =

Explanation:

Step1: Use parallelogram property

In a parallelogram, opposite - sides are equal. So, $BC = DE$ and $CD = BE$. Here, $BC=x$ and $DE = 6x - 95$, and $CD=7x - 91$ and $BE$ is not given in terms of $x$ but we use the fact that $BC = DE$. Set up the equation $x=6x - 95$.
$x=6x - 95$

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $0 = 6x-x - 95$, which simplifies to $0 = 5x - 95$. Then add 95 to both sides: $5x=95$. Divide both sides by 5: $x = 19$.
$5x=95\Rightarrow x = 19$

Step3: Find the length of $CD$

Substitute $x = 19$ into the expression for $CD$. $CD=7x - 91$.
$CD=7\times19 - 91=133 - 91 = 42$

Step4: Find the length of $BC$

Since $BC=x$, and $x = 19$, then $BC = 19$.

Answer:

$CD = 42$
$BC = 19$