[tex]f=6cm\\g=8cm[/tex]
Why?
The first thing we need to do is find the area of the triangle, we can to that by subtracting the area of ABCD from ACBE, then, we can use the formulas to calculate the area for both triangle and rectangle to find "f" and "g".
Calculating we have:
[tex]TriangleArea=ABCE-ABCD\\\\TriangleArea=60cm^{2}-48cm^{2}=12cm^{2}[/tex]
Now, we can calculate "f" by using the formula to calculate the area of the triangle:
[tex]TriangleArea=\frac{b*h}{2}\\\\TriangleArea=\frac{f*4cm}{2}\\\\12cm^{2}*2=f*4cm\\\\\frac{24cm^{2}}{4cm}=f\\\\f=6cm[/tex]
Now, finding "g" by using the formula to calculate the area of the rectangle, we have:
[tex]RectangleArea=ABCD\\\\ABCD=Base*Height\\\\48cm^{2}=base*6cm\\\\base=g=\frac{48cm^{2}}{6cm}=8cm[/tex]
Hence, we have that:
[tex]f=6cm\\g=8cm[/tex]
Have a nice day!
