Answer:
8 in
Step-by-step explanation:
Let the length of AB be x in:
[tex]AB = BC = BF = FE=x \ in[/tex]
Area of the triangular part is calculated as:
[tex]A_t=\frac{1}{2}bh\\\\=\frac{1}{2}\times x \times x \\\\=0.5x \ in^2[/tex]
Area go the rectangular part is calculated as:
[tex]A=lw\\\\=x\times 2x\\\\=2x^2 \ in^2[/tex]
The total area is given as 160 sq in. We equate this to the two areas to solve for x:
[tex]A=lw+0.5bh\\\\160=2x^2+0.5x^2\\\\x^2=\frac{160}{2.5}=64\\\\x=8 \ in[/tex]
Hence, the length of AB is 8 in
