High School

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Karim builds a wooden table. The rectangular top of his table has an area of [tex]$3^7$[/tex] square inches and a length of [tex]$3^4$[/tex] inches. What is the width of the table top?

A. 9 inches
B. 27 inches
C. 2,187 inches
D. 59,049 inches

Answer :

To find the width of the table top, we need to use the relationship between the area, length, and width of a rectangle. The formula for the area of a rectangle is [tex]\( \text{Area} = \text{Length} \times \text{Width} \)[/tex].

Here are the given values:
- The area of the table top is [tex]\( 3^7 \)[/tex] square inches.
- The length of the table top is [tex]\( 3^4 \)[/tex] inches.

Our task is to find the width of the table top. We can use the formula to solve for the width:

1. Calculate the Area:
[tex]\[
3^7 = 2187 \text{ square inches}
\][/tex]

2. Calculate the Length:
[tex]\[
3^4 = 81 \text{ inches}
\][/tex]

3. Use the Formula for Width:
[tex]\[
\text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{2187}{81}
\][/tex]

4. Simplify to Find the Width:
[tex]\[
\text{Width} = 27 \text{ inches}
\][/tex]

Therefore, the width of the table top is 27 inches.

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