Question 11 of 25

The ratio of the surface areas of two similar solids is [tex]49:100[/tex]. What is the ratio of their corresponding side lengths?

A. [tex]7:10[/tex]
B. [tex]\frac{49}{10}:10[/tex]
C. [tex]7:\frac{100}{7}[/tex]
D. [tex]1:24[/tex]



Answer :

To find the ratio of the corresponding side lengths of the two similar solids, given that the ratio of their surface areas is \(49:100\), we can follow these steps:

1. Understand the relationship between surface area and side length in similar solids:
- For similar solids, the ratio of their surface areas is the square of the ratio of their corresponding side lengths.

2. Express the given information:
- The ratio of the surface areas is given as \(49:100\).
- Let the ratio of the side lengths be \(a:b\).

3. Set up the relationship using the given ratio:
- Since the ratio of the surface areas is \(49:100\), this can be written as:
[tex]\[ \left(\frac{a}{b}\right)^2 = \frac{49}{100} \][/tex]

4. Solve for the ratio of the side lengths:
- To find the ratio of the side lengths, we need to take the square root of both sides:
[tex]\[ \frac{a}{b} = \sqrt{\frac{49}{100}} \][/tex]
- The square root of 49 is 7.
- The square root of 100 is 10.
- Therefore, the ratio of the side lengths is:
[tex]\[ \frac{a}{b} = \frac{7}{10} \][/tex]

5. Express the ratio in simplest form:
- The simplest form of the ratio \(7:10\) is just \(7:10\).

Therefore, the correct answer is:
[tex]\[ \boxed{A. \; 7:10} \][/tex]