ANSWER:
64 square inches.
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the ratio between the corresponding sides of the triangles:
[tex]r=\frac{8}{6}=\frac{4}{3}[/tex]
We must bear in mind that the area of the larger t triangle is equal to the area of the small triangle multiplied by the ratio of the square, since the area is a quadratic unit, therefore:
[tex]\begin{gathered} A_2=r^2\cdot A_1 \\ \text{ we replacing} \\ A_2=\mleft(\frac{4}{3}\mright)^2\cdot36=\frac{4^2}{3^2}\cdot36=\frac{16}{9}\cdot36 \\ A_2=64in^2 \end{gathered}[/tex]
The area of the larger triangle is 64 square inches.
