Question

the figures below are similar. the labeled sides are corresponding. what is the area of the larger triangle?

Answer 1

64 square inches.

Explanation:

The first thing is to calculate the ratio between the corresponding sides of the triangles:

`r=(8)/(6)=(4)/(3)`

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:

`\begin{gathered} A_2=r^2\cdot A_1 \\ \text{ we replacing} \\ A_2=\mleft((4)/(3)\mright)^2\cdot36=(4^2)/(3^2)\cdot36=(16)/(9)\cdot36 \\ A_2=64in^2 \end{gathered}`

The area of the larger triangle is 64 square inches.