Question

2. You are making wooden picture
frames of different sizes but you
have limited supplies, so you are
restricting the perimeter of each
frame to 4 feet or less and the length
to exactly 1.5 feet. Find the range of
the frame width. Show your work.

Answer 1

The range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.

What is the range of a particular data set?

For a set of data, the range is the difference between the maximum and minimum value. It sort of gives an idea of spread of the data.

For this case, we're given that:

• Frame is rectangular (assumingly).
• The perimeter of the frame ≤ 4 feet
• The length of the frame = 1.5 feet

Perimeter of a rectangle = 2(length + width)

Let 'l' denotes length, and 'w' denotes width, then we get:

$Perimeter \leq 4\\2(l+w) \leq 4\\2(1.5 + w) \leq 4\\\\\text{Dividing both the sides by 2}\\\\1.5 + w \leq 2\\\\\text{Subtracting 1.5 from both the sides so as to get 'w' on one side}\\\\w \leq 0.5$

Now since the lowest value of width of a frame can be zero only, therefore, we get:

$0 \leq w \leq 0.5$

Thus, the range of values 'w' can assume is: 0.5 - 0 = 0.5

Thus, the range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.

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