Question

Given:• AABC ~ AFGH• AB = 15 inches• FG = 10 inches• The perimeter of AABC is 36 inches.• The area of AABC is 45 square inches.The perimeter of AFGH isinches.The area of AFGH issquare inches.

Answer 1

The two triangles, ABC and FGH are congruent.

The length of two corresponding sides are given,

`\begin{gathered} \text{If }\Delta ABC\cong\Delta FGH \\ \text{Then,} \\ AB\cong FG \\ \text{If AB=15, and FG=10} \\ \text{Then} \\ \text{Ratio}=(FG)/(AB) \\ \text{Ratio}=(2)/(3) \end{gathered}`

If the ratio of the sides is determined as 2/3, then the perimeter which is an addition of all three sides shall be;

`\begin{gathered} AB=15 \\ FG=(2)/(3)*15 \\ \text{Similarly,} \\ \text{Perimeter }\Delta ABC=36 \\ \text{Perimeter }\Delta FGH=(2)/(3)*36 \\ \text{Perimeter }\Delta FGH=24in \end{gathered}`

To determine the area, we shall apply the ratio raied to the power of 2 (becaue the area i in units squared).

Therefore, we would have;

`\begin{gathered} \text{Area }\Delta ABC=45in^2 \\ \text{Area }\Delta FGH=45*((2)/(3))^2 \\ \text{Area }\Delta FGH=45*(4)/(9) \\ \text{Area }\Delta FGH=20in^2 \end{gathered}`

Therefore, the perimeter of triangle FGH is 24 inches

The area of triangle FGH is 20 inches squared