Question

can ahmed use the larger sheets of paper shown to make paper cutouts similar to his original hummingbird cutout? if not, how can he trim the sheets of paper so he can use them? justify your answer.

a. ahmed cannot use either sheet of paper because neither sheet has side lengths that are proportional to his cutout. he can use the 3 ft - by - 4 ft sheet of paper if he cuts it down to 3 ft - by - ft. he can use the 120 cm - by - 180 cm sheet of paper if he cuts it down to 120 cm - by - cm.
(type an integer or a decimal.)
b. ahmed can use the 3 ft - by - 4 ft sheet of paper without trimming it because the side lengths are proportional to his cutout. he can use it if he cuts it down to 120 cm - by - cm.
(type an integer or a decimal.)
c. ahmed can use the 120 - cm by - 180 cm sheet of paper without trimming it because the side lengths are proportional to his cutout. the 3 ft - by - 4 ft sheet of paper does not have side lengths that are proportional to his cutout. he can use it if he cuts it down to 3 ft - by - ft.

Explanation:

Step1: Calculate the ratio of the original cutout

The original cutout has dimensions \(12\) in by \(9\) in. The ratio of length to width is \(\frac{12}{9}=\frac{4}{3}\)

Step2: Check the ratio of the \(3\) ft - by -\(4\) ft sheet

Since \(1\) ft \( = 12\) in, \(3\) ft \(=3\times12 = 36\) in and \(4\) ft \(=4\times12=48\) in. The ratio of length to width is \(\frac{48}{36}=\frac{4}{3}\)

Step3: Check the ratio of the \(120\) cm - by -\(180\) cm sheet

The ratio of length to width is \(\frac{180}{120}=\frac{3}{2}
eq\frac{4}{3}\)

Let the width of the trimmed \(120\) cm - by -\(x\) cm sheet be \(x\). Using the proportion \(\frac{120}{x}=\frac{4}{3}\), cross - multiply: \(4x = 120\times3\), so \(x = 90\)

Answer:

A. Ahmed cannot use either sheet of paper because neither sheet has side lengths that are proportional to his cutout. He can use the \(3\) ft - by -\(4\) ft sheet of paper if he cuts it down to \(3\) ft - by -\(3\) ft. He can use the \(120\) cm - by -\(180\) cm sheet of paper if he cuts it down to \(120\) cm - by -\(90\) cm.