Question
The areas of two squares have a ratio of \( 1: 4 \). The larger square has an area of 400 squar inches. What is the side length of the smaller square?
Ask by Mcfarlane Fuentes. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The side length of the smaller square is 10 inches.
Solution
Given:
- The ratio of the areas of two squares is \( 1:4 \).
- The larger square has an area of 400 square inches.
Let's denote:
- \( A_s \) as the area of the smaller square.
- \( A_l \) as the area of the larger square.
From the ratio:
\[
\frac{A_s}{A_l} = \frac{1}{4}
\]
Substituting \( A_l = 400 \) square inches:
\[
A_s = \frac{1}{4} \times 400 = 100 \text{ square inches}
\]
The side length \( s \) of a square is the square root of its area:
\[
s = \sqrt{A_s} = \sqrt{100} = 10 \text{ inches}
\]
**Answer:** 10 inches
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Since the area of the larger square is 400 square inches and the ratio of the areas is \( 1: 4 \), the area of the smaller square can be calculated as follows: If the area of the larger square is \( 4x \) and equals 400, then \( 4x = 400 \). Solving for \( x \), we divide both sides by 4 to get \( x = 100 \). Now, the area of the smaller square is 100 square inches. The side length of a square is the square root of its area. Therefore, the side length of the smaller square is: \[ \sqrt{100} = 10 \text{ inches}. \] So, the side length of the smaller square is 10 inches.
