Answer:
a = 8
Step-by-step explanation:
The following inequalities will form a rectangle. Hence, the area of a rectangle is [tex]\displaystyle{A=\Delta x \cdot \Delta y}[/tex]
In this case, [tex]\Delta x[/tex] = 5-1 which is 4, and [tex]\Delta y[/tex] = a - 2. Substitute in:
[tex]\displaystyle{24 = 4\cdot (a-2)}[/tex]
Now solve the equation for a-term:
[tex]\displaystyle{24=4a-8}\\\\\displaystyle{24+8=4a}\\\\\displaystyle{32=4a}\\\\\displaystyle{8=a}[/tex]
Therefore, the value of a is 8 to make the region have an area of 24 square units.
