Question

Sophia bought 3 yards of trim to put around a rectangular scarf. She wants the width of the scarf to be a whole number that is at least 6 inches and at most 12 inches. If she uses all the trim,wh Write your answers in inchesat are the possible dimensions of her scarf?

Answer 1

possible dimensions of the scarf are:
Width:6 inches Length:96inches
Width:12 inches Length:84 inches
Width:11inches Length: 86 inches
Width:10 inches Length: 88 inches
Width: 7 inches Length: 94 inches
Width: 8 inches Length: 92 inches
Width: 9 inches Length: 90 inches

Answer 2

The length of the scarf is at least 42 inches and at most 48 inches.

Explanation:

We are given the following information:

Length of trim = 3 yards = 108 inches

The width of the scarf to be a whole number that is at least 6 inches and at most 12 inches.

Let w be the width of the scarf and l be the length of scarf.

Perimeter of scarf =

`\text{Permiter of rectangle} = 2(l+w)`

Then, we can write:

`6 \leq w \leq 12\\6+l \leq w+l \leq 12+l\\2(6+l) \leq 2(l+w) \leq 2(12+l)\\2(6+l) \leq \text{Perimeter of scarf}) \leq 2(12+l)\\2(6+l) \leq 108 \leq 2(12+l)\\\Rightarrow 2(6+l) \leq 108\\12 + 2l \leq 108\\l \leq 48\\\rightarrow 108 \leq 2(12+l)\\108 \leq 24 + 2l\\l \geq 42\\\Rightarrow 42 \leq l \leq 48`

The length of the scarf is at least 42 inches and at most 48 inches.