Question

Use this proportion to solve for the area of the small card. (Look at the pictures provided)

Answer 1

Given:

The area of the big card = 384 square in.

And the side of the big card = 24 in.

The side of the small card = 8 in.

Required:

Use this to find the area of the small card.

Step-by-step explanation:

The given formula is:fi

`\frac{Area\text{ of big card}}{Area\text{ of small card}}=(\frac{side\text{ of big card}}{side\text{ of small card}})^2`

Substitute the given values in the formula:

`\begin{gathered} \frac{384}{Area\text{ of small card}}=((24)/(8))^3 \\ \frac{384}{Area\text{ of small card}}=(3)^2 \\ \frac{384}{Area\text{ of small card}}=9 \end{gathered}`
`\begin{gathered} Area\text{ of small card = }(384)/(9) \\ =42.67\text{ in}^2 \end{gathered}`

Final Answer:

The area of the small card is

`42.67\text{ in}^2`