Question

In the figure, ABCD and EFGF are rectangle. ABCD and EFGH are similar.(a) If the length of AB is a cm, try to use a to Indicate the length of EF(b) Find the ratio of the areas of ABCD and EFGH.(English isn't my native language. Please correct me if I have any grammatical mistakes.)

Answer 1

Given:

BC = 3 cm, FG = 4 cm

Required: bLength of EF and ratio of areas

Step-by-step explanation:

(a) Since the rectangles ABCD and EFGH are similar, the correponding angles are proportional. Hence

`(AB)/(EF)=(BC)/(FG)`

Plug the given values.

`(AB)/(EF)=(3)/(4)`

If AB = a cm, then

`\begin{gathered} (a)/(EF)=(3)/(4) \\ EF=(4a)/(3) \end{gathered}`

(b) Ara of ABCD

`\begin{gathered} =\text{ Length}*\text{ Width} \\ =3a\text{ cm}^2 \end{gathered}`

Area of EFGH

`\begin{gathered} =\text{ Length}*\text{ Width} \\ =4*(4a)/(3) \\ =(16a)/(3)\text{ cm}^2 \end{gathered}`

Ratio of areas

`\begin{gathered} =3a:(16a)/(3) \\ =9:16 \end{gathered}`

Final Answer: The ratio of areas of ABCD to EFGH is 916.