Explanation:
We are not told if both triangles have same areas.
So we would be assuming the triangles are similiar triangles
One of the triangle's dimension:
Base = 10 in, height = 12 in
The 2nd triangle's dimension:
height = 4in, base = ?
We apply the ratio of the corresponding sides of the triangles:
base/height of 1st triangle = Base/Height 2nd triangle
[tex]\begin{gathered} \frac{10}{12}=\frac{Base}{4} \\ 10\times4=\text{ 12}\times Base \end{gathered}[/tex][tex]\begin{gathered} 40\text{ = 12Base} \\ \text{divide both sides by 12:} \\ \frac{40}{12\text{ }}=\text{ Base} \\ \text{Base = }\frac{10}{3} \\ \text{Base = 3}\frac{1}{3}\text{ in (option A)} \end{gathered}[/tex]