To find the area of the second triangle when its side lengths are 5 times those of the first triangle, we need to consider the properties of similar triangles.
### Step-by-Step Solution:
1. Understanding Similar Triangles:
When two triangles are similar, their corresponding sides are in proportion. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding side lengths.
2. Given Data:
- The area of the first triangle, [tex]\( A_1 = 8 \)[/tex] square units.
- The side lengths of the second triangle are 5 times those of the first triangle.
3. Ratio of Side Lengths:
The ratio of the side lengths between the second triangle and the first triangle is 5:1.
4. Area Ratio for Similar Triangles:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding side lengths. Therefore, the ratio of the areas can be calculated as:
[tex]\[
\left(\text{Side length ratio}\right)^2 = 5^2 = 25
\][/tex]
5. Calculating the Area of the Second Triangle:
Since the area of the second triangle is 25 times the area of the first triangle, we can multiply the area of the first triangle by 25 to find the area of the second triangle:
[tex]\[
A_2 = A_1 \times 25
\][/tex]
Substituting the known value:
[tex]\[
A_2 = 8 \times 25 = 200 \text{ square units}
\][/tex]
### Conclusion:
The area of the second triangle is [tex]\( 200 \)[/tex] square units.
