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 5 and 4 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,

$2x+2y=18$

Step 2. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

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

$2x+5y=30$

Step 3. Description of step.

Subtract the equation in step 1 from the equation in step 2.

$\begin{array}{c}2x+5y-\left(2x+2y\right)=30-18\\ 2x+5y-2x-2y=12\\ 3y=12\\ y=4\end{array}$

Step 4. Description of step.

Substitute 4 for y into $2x+2y=18$ to find the value of x.

$\begin{array}{c}2x+2\times 4=18\\ 2x+8=18\\ 2x=10\\ x=5\end{array}$

Therefore, the value of x and y is 5 and 4 respectively.