Answer:
base = 8 cm
step-by-step explanation:
Let the base be "b"
Then the height will be "3b + 8"
Therefore use the following to find area:
[tex]\rightarrow \sf \frac{1}{2} * base * height = area \ of \ triangle[/tex]
[tex]\rightarrow \sf \frac{1}{2} * b* (3b+8)= 128[/tex]
[tex]\rightarrow \sf \frac{1}{2} * b* (3b+8)= 128[/tex]
[tex]\rightarrow \sf 3b^2+8b= 128*2[/tex]
[tex]\rightarrow \sf 3b^2+8b=256[/tex]
[tex]\rightarrow \sf 3b^2+8b-256=0[/tex]
[tex]\rightarrow \sf 3b^2+32b-24b-256=0[/tex]
[tex]\rightarrow \sf b(3b+32)- 8(3b+32) =0[/tex]
[tex]\rightarrow \sf (b- 8)(3b+32) =0[/tex]
[tex]\rightarrow \sf b = 8, \ -\dfrac{32}{3}[/tex]
Therefore "b", base is 8 cm and height = 3(8) + 8 = 32 cm
