Question

9) If AD = 3x + 4 and BC = x+15. thenx = & AD = E A D

Answer 1

In a parallelogram, opposite sides are equal. This means that AD=BC.

Since AD=3x+4 and BC=x+15, we have

`3x+4=x+15`

If we move x to the left hand side as -x and 4 to the right hand side as -4, we obtain,

`3x-x=15-4`

then, x is equal to

`\begin{gathered} 2x=11 \\ x=(11)/(2) \end{gathered}`

Now, we must substitute this values into AD and BC. We have for AD,

`\begin{gathered} AD=3x+4 \\ AD=3\cdot(11)/(2)+4 \\ AD=(33)/(2)+4 \\ AD=(33)/(2)+(8)/(2) \\ AD=(33+8)/(2) \\ AD=(41)/(2) \end{gathered}`

and for BC, we have

`\begin{gathered} BC=x+15 \\ BC=(11)/(2)+15 \\ BC=(11)/(2)+(30)/(2) \\ BC=(11+30)/(2) \\ BC=(41)/(2) \end{gathered}`

which is an expected result because AD=BC. However, its a checking for our computations.

In summary, the answers are:

`\begin{gathered} x=(11)/(2) \\ AD=BC=(41)/(2) \end{gathered}`