Answer:
The values of [tex]f[/tex] and [tex]g[/tex] are, respectively:
[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]
Step-by-step explanation:
The area of the triangle ADE is:
[tex]A_{ADE} = 60\,cm^{2}-48\,cm^{2}[/tex]
[tex]A_{ADE} = 12\,cm^{2}[/tex]
The area of the triangle is defined by the following formula:
[tex]A_{ADE} = \frac{1}{2}\cdot AD\cdot DE[/tex] (1)
If we know that [tex]A_{ADE} = 12\,cm^{2}[/tex] and [tex]DE = 4\,cm[/tex], then the length of the line segment [tex]AD[/tex] is:
[tex]AD = \frac{2\cdot A_{ADE}}{DE}[/tex]
[tex]AD = 6\,cm[/tex]
And the area of the rectangle is:
[tex]A_{ABCD} = AD\cdot CD[/tex] (2)
If we know that [tex]A_{ABCD} = 48\,cm^{2}[/tex] and [tex]AD = 6\,cm[/tex], then the length of the line segment [tex]CD[/tex] is:
[tex]CD = \frac{A_{ABCD}}{AD}[/tex]
[tex]CD = 8\,cm[/tex]
Hence, the values of [tex]f[/tex] and [tex]g[/tex] are, respectively:
[tex]f = 6\,cm[/tex], [tex]g = 8\,cm[/tex]
