Question
The area of a mirror is 225 square inches, and its width is 13 3/4 inches, will the mirror fit in a space that is 15 inches by 16 inches
Answers
GPT-4o mini
To determine if the mirror will fit in a space of 15 inches by 16 inches, we first need to find the dimensions of the mirror based on its area and width.
The area of the mirror is given as 225 square inches, and the width is given as 13 3/4 inches.
1. First, let's convert 13 3/4 inches to an improper fraction or a decimal for easier calculations.
\[
13 \frac{3}{4} = 13 + \frac{3}{4} = \frac{52}{4} + \frac{3}{4} = \frac{55}{4} \text{ inches} = 13.75 \text{ inches}
\]
2. Next, we can find the height of the mirror using the formula for the area:
\[
\text{Area} = \text{Width} \times \text{Height}
\]
Rearranging this to solve for height gives:
\[
\text{Height} = \frac{\text{Area}}{\text{Width}} = \frac{225}{13.75}
\]
Now, performing the division:
\[
\text{Height} = \frac{225}{13.75} = 16.36 \text{ inches (approximately)}
\]
3. Now we have the dimensions of the mirror:
- Width: 13.75 inches
- Height: 16.36 inches
4. Next, we need to check if these dimensions will fit into the given space of 15 inches by 16 inches.
- The width of the mirror (13.75 inches) is less than the width of the space (15 inches).
- The height of the mirror (16.36 inches) is greater than the height of the space (16 inches).
Since the height of the mirror exceeds the height of the available space, **the mirror will not fit in the space of 15 inches by 16 inches.**
The area of the mirror is given as 225 square inches, and the width is given as 13 3/4 inches.
1. First, let's convert 13 3/4 inches to an improper fraction or a decimal for easier calculations.
\[
13 \frac{3}{4} = 13 + \frac{3}{4} = \frac{52}{4} + \frac{3}{4} = \frac{55}{4} \text{ inches} = 13.75 \text{ inches}
\]
2. Next, we can find the height of the mirror using the formula for the area:
\[
\text{Area} = \text{Width} \times \text{Height}
\]
Rearranging this to solve for height gives:
\[
\text{Height} = \frac{\text{Area}}{\text{Width}} = \frac{225}{13.75}
\]
Now, performing the division:
\[
\text{Height} = \frac{225}{13.75} = 16.36 \text{ inches (approximately)}
\]
3. Now we have the dimensions of the mirror:
- Width: 13.75 inches
- Height: 16.36 inches
4. Next, we need to check if these dimensions will fit into the given space of 15 inches by 16 inches.
- The width of the mirror (13.75 inches) is less than the width of the space (15 inches).
- The height of the mirror (16.36 inches) is greater than the height of the space (16 inches).
Since the height of the mirror exceeds the height of the available space, **the mirror will not fit in the space of 15 inches by 16 inches.**