Answer:
2.9 in.
Step-by-step explanation:
Let x in be the width of the larger rectangle. If the length of the larger rectangle is 4 inches and the perimeter of the larger rectangle is 14 in, then
[tex]x+4+x+4=14,\\ \\2x=14-8,\\ \\2x=6,\\ \\x=3\ in.[/tex]
If two rectangles are similar, then their lengths and widths are proportional with the scale factor k. Thus, the length of the smaller rectangle is [tex]4k[/tex] in and the width of the smaller rectangle is [tex]3k[/tex] in. If the perimeter of the smaller rectangle is 10 in, then
[tex]4k+3k+4k+3k=10,\\ \\14k=10,\\ \\k=\dfrac{10}{14}=\dfrac{5}{7},\\ \\4k=\dfrac{20}{7}\approx 2.9\ in,\\ \\3k=\dfrac{15}{7}\approx 2.1\ in.[/tex]
