Question

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short answer

The value of x and y is 7 and 18 respectively.

Step-by-step solution

Step 1. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

In a given figure, by the property of a parallelogram,

$\begin{array}{c}3x+4=25;\\ 2y-8=28\end{array}$

Step 2. Description of step.

Subtract 4 from both sides of $3x+4=25$.

$\begin{array}{c}3x+4-4=25-4\\ 3x=21\end{array}$

Step 3. Description of step.

Divide each side of $3x=21$ by 3 to obtain the value of x.

$\begin{array}{c}\frac{3x}{3}=\frac{21}{3}\\ x=7\end{array}$

Step 4. Description of step.

Add 8 on both sides of $2y-8=28$.

$\begin{array}{c}2y-8+8=28+8\\ 2y=36\end{array}$

Step 5. Description of step.

Divide each side of $2y=36$ by 2 to obtain the value of y.

$\begin{array}{c}\frac{2y}{2}=\frac{36}{2}\\ y=18\end{array}$

Therefore, the value of x and y is 7 and 18 respectively.