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 10 and 16 respectively.

Step-by-step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

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

$\begin{array}{c}2x+y=36;\\ 4x-y=24\end{array}$

Step 2. Description of step.

Add equations in step 1.

$\begin{array}{c}2x+y+4x-y=36+24\\ 6x=60\end{array}$

Step 3. Description of step.

Divide each side of $6x=60$ by 6 to obtain the value of x.

$\begin{array}{c}\frac{6x}{6}=\frac{60}{6}\\ x=10\end{array}$

Step 4. Description of step.

Substitute 10 for x into $2x+y=36$ to find the value of y.

$\begin{array}{c}2\times 10+y=36\\ 20+y=36\\ y=36-20\\ =16\end{array}$

Therefore, the value of x and y is 10 and 16 respectively.