Question

kiara is designing a newsletter. she has a rectangular picture that is 6 inches high and 4 inches wide, and she wants to enlarge the picture so that it will fit into a rectangular space that is 9 inches high and 8 inches wide. if kiara makes the enlarged picture as large as possible, what is the area of this enlarged picture? 1 of 3 question 96 in² 63 in² 72 in² 54 in²

Explanation:

Step1: Calculate the height - width ratios

The ratio of the original picture: $\frac{6}{4}=\frac{3}{2}$.
The ratio of the space: $\frac{9}{8}$.
Since $\frac{3}{2}>\frac{9}{8}$, the height of the enlarged picture will be limited by the height of the space.

Step2: Calculate the width of the enlarged picture

Let the width of the enlarged picture be $x$.
Using the proportion of similar rectangles (based on height - width ratio of the original picture), $\frac{6}{4}=\frac{9}{x}$.
Cross - multiply: $6x = 4\times9$.
Solve for $x$: $x=\frac{4\times9}{6}=6$.

Step3: Calculate the area of the enlarged picture

The area formula for a rectangle is $A = h\times w$.
Here, $h = 9$ inches and $w = 6$ inches.
So, $A=9\times6 = 54$ $in^{2}$.

Answer:

54 $in^{2}$ (the fourth option)