Question

Quad. DECK is a parallelogram. Complete.

If $\mathrm{KT}=2\mathrm{x}+\mathrm{y},\mathrm{DT}=\mathrm{x}+2\mathrm{y},\mathrm{TE}=12$and $\mathrm{TC}=9$, then$\mathrm{x}=?$ and$\mathrm{y}=?$

Short answer

The value of x and y is 5 and 2 respectively.

Step-by-step solution

Step 1. Consider the following diagram.

Step 2. 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,

$\begin{array}{c}x+2y=9;\\ 2x+y=12\end{array}$

Step 3. Description of step.

Multiply equation $2x+y=12$by 2.

$\begin{array}{c}2\left(2x+y\right)=2\times 12\\ 4x+2y=24\end{array}$

Step 4. Description of step.

Subtract $x+2y=9$from $4x+2y=24$.

$\begin{array}{c}4x+2y-x-2y=24-9\\ 3x=15\\ x=5\end{array}$

Step 5. Description of step.

Substitute 5 for x into $2x+y=12$ to find the value of y.

$\begin{array}{c}2\times 5+y=12\\ 10+y=12\\ y=12-10\\ =2\end{array}$

Therefore, the value of x and y is 5 and 2 respectively.