Answer:
D) The Length of the rectangle is [tex]1\frac{1}{2}x + 4[/tex]
Step-by-step explanation:
Here, the width of the rectangle = [tex]\frac{1}{4}x + 5[/tex]
Let the length of the rectangle = L
Also, given the perimeter of the figure = [tex]3( \frac{1}{2}) x + 18[/tex]
Now we know that, Perimeter of the Rectangle = 2(Length + Width)
or, [tex]3( \frac{1}{2}) x + 18 = 2(L + \frac{1}{4}x + 5)[/tex]
Solving for L, we get :
[tex]2L + \frac{x}{2} + 10 = \frac{3x}{2} +18\\ or, 2L = \frac{3x}{2} - \frac{x}{2} + 18 -10\\or, L = \frac{2x}{2} + \frac{8}{2}[/tex]
Hence the length of the rectangle is , D) [tex] 1\frac{1}{2}x + 4[/tex]
