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A piece of paper is to display 128 square inches of text. If there are to be one-inch margins on both sides and two-inch margins at the bottom and top, what are the dimensions of the smallest piece of paper (by area) that can be used? Choose 1 answer: (A) 8''×16'' (B) 10'×15' (C) 10'×18' (D) 10'×20' (E) None of these

A piece of paper is to display 128128 square inches of text. If there are to be one-inch margins on both sides and two-inch margins at the bottom and top, what are the dimensions of the smallest piece of paper (by area) that can be used?\newlineChoose 11 answer:\newline(A) 8′′×16′′ 8 \prime \prime \times 16 \prime \prime \newline(B) 10′′×15′′ 10 \prime \prime \times 15 \prime \prime \newline(C) 10′′×18′′ 10 \prime \prime \times 18 \prime \prime \newline(D) 10′′×20′′ 10 \prime \prime \times 20 \prime \prime \newline(E) None of these

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Q. A piece of paper is to display 128128 square inches of text. If there are to be one-inch margins on both sides and two-inch margins at the bottom and top, what are the dimensions of the smallest piece of paper (by area) that can be used?\newlineChoose 11 answer:\newline(A) 8′′×16′′ 8 \prime \prime \times 16 \prime \prime \newline(B) 10′′×15′′ 10 \prime \prime \times 15 \prime \prime \newline(C) 10′′×18′′ 10 \prime \prime \times 18 \prime \prime \newline(D) 10′′×20′′ 10 \prime \prime \times 20 \prime \prime \newline(E) None of these
  1. Calculate Side Margins: First, let's calculate the total width of the margins on both sides. Since there's a one-inch margin on each side, that's 11 inch + 11 inch = 22 inches total for the side margins.
  2. Calculate Top and Bottom Margins: Next, calculate the total height of the margins at the bottom and top. There's a two-inch margin at the bottom and top, so that's 22 inches + 22 inches = 44 inches total for the top and bottom margins.
  3. Find Paper Dimensions: Now, we need to add the width of the margins to the width of the text area and the height of the margins to the height of the text area to get the dimensions of the paper. Let's call the width of the text area WW and the height HH. So the dimensions of the paper would be (W+2)(W + 2) by (H+4)(H + 4).
  4. Calculate Text Area: Since the area of the text is 128128 square inches, we have W×H=128W \times H = 128. We need to find values of WW and HH that when multiplied give 128128 and, when increased by the margins, give us the smallest possible area for the paper.
  5. Test Option (A): Looking at the answer choices, we can start by testing them to see which one fits our requirements. Let's start with option (A) 8′′×16′′8''\times16''. If we subtract the margins, the text area would be (8−2)(8 - 2) inches by (16−4)(16 - 4) inches, which is 66 inches by 1212 inches. But 6×12=726 \times 12 = 72, not 128128.
  6. Test Option (B): Next, let's try option (B) 10′×15′10'\times15'. Subtracting the margins, the text area would be (10−2)(10 - 2) inches by (15−4)(15 - 4) inches, which is 88 inches by 1111 inches. But 8×11=888 \times 11 = 88, which is also not 128128.
  7. Test Option (C): Now, let's try option (C) 10′×18′10'\times18'. Subtracting the margins, the text area would be (10−2)(10 - 2) inches by (18−4)(18 - 4) inches, which is 88 inches by 1414 inches. But 8×14=1128 \times 14 = 112, which is still not 128128.
  8. Test Option (D): Let's try option (D) 10′×20′10'\times20'. Subtracting the margins, the text area would be (10−2)(10 - 2) inches by (20−4)(20 - 4) inches, which is 88 inches by 1616 inches. And 8×16=1288 \times 16 = 128, which is correct. So the dimensions of the paper are 1010 inches by 2020 inches.

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