Question

A rectangle has a perimeter of 14 inches. A similar rectangle has a perimeter of 10 inches. If the length of the larger rectangle is 4 inches, what is the length of the smaller rectangle? Round to the nearest tenth

Answer 1

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

$x+4+x+4=14,\\ \\2x=14-8,\\ \\2x=6,\\ \\x=3\ in.$

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 $4k$ in and the width of the smaller rectangle is $3k$ in. If the perimeter of the smaller rectangle is 10 in, then

$4k+3k+4k+3k=10,\\ \\14k=10,\\ \\k=\dfrac{10}{14}=\dfrac{5}{7},\\ \\4k=\dfrac{20}{7}\approx 2.9\ in,\\ \\3k=\dfrac{15}{7}\approx 2.1\ in.$