A piece of paper is to display $150$ square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used? $\newline$ Choose $1$ answer: $\newline$ (A) $6 \prime \prime 25 \prime \prime$ $\newline$ (B) $10 \prime \times 15 \prime$ $\newline$ (C) $12 \prime \times 18 \prime$ $\newline$ (D) $15 \prime \prime 18 \prime$ $\newline$ (E) None of these

View step-by-step help

Home

Math Problems

Grade 6

Prime factorization

Full solution

Q. A piece of paper is to display

150

square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?

\newline

Choose

1

answer:

\newline

(A)

6 \prime \prime 25 \prime \prime

\newline

(B)

10 \prime \times 15 \prime

\newline

(C)

12 \prime \times 18 \prime

\newline

(D)

15 \prime \prime 18 \prime

\newline

(E) None of these

Identify margin space: Identify the total margin space required on each side of the text. There is a $1$ -inch margin on each side and the top, and a $2$ -inch margin at the bottom.
Calculate horizontal margin: Calculate the total horizontal margin. There are two sides, each with a one-inch margin, so the total horizontal margin is $1$ inch + $1$ inch = $2$ inches.
Calculate vertical margin: Calculate the total vertical margin. There is a one-inch margin at the top and a two-inch margin at the bottom, so the total vertical margin is $1$ inch + $2$ inches = $3$ inches.
Determine text area dimensions: Determine the dimensions of the text area without the margins. Since the text area is $150$ square inches, we need to find two numbers (width and height) that multiply to $150$ . The factors of $150$ that are closest to each other are $10$ and $15$ .
Add margins to dimensions: Add the margins to the dimensions of the text area to find the dimensions of the paper. The width of the text area is $10$ inches, and the height is $15$ inches. Adding the horizontal margins gives a width of $10$ inches $+$ $2$ inches $=$ $12$ inches. Adding the vertical margins gives a height of $15$ inches $+$ $3$ inches $=$ $15$ $1$ inches.
Check calculated paper dimensions: Check if the calculated dimensions of the paper match any of the given choices. The calculated dimensions are $12$ inches by $18$ inches, which matches choice $(C)$ .