Final answer:
To find the area of the larger rectangle, square the ratio of the lengths (5:8 to find the area ratio, 25:64), and then use a proportion to solve for the area of the larger rectangle, which is approximately 133 m² when rounded to the nearest whole number.
Step-by-step explanation:
To find the area of the larger rectangle when given that the ratio of the length of the corresponding sides of two rectangles is 5:8 and the area of the smaller rectangle is 130 m², we can use the rule that the ratio of areas of similar figures is the square of the scale factor. In this example, if the scale factor for the sides is 5:8, then the scale factor for the area will be the square of that ratio.
First, calculate the area scale factor by squaring the ratio of the lengths. Since the sides ratio is 5:8, the area ratio is (5²):(8²), which simplifies to 25:64. Knowing the area of the smaller rectangle, we can set up a proportion to find the area of the larger rectangle:
25/64 = 130/x
Multiply both sides of the equation by x, and then by 64, to solve for x, which represents the area of the larger rectangle:
25x = 64 × 130
x = (64 × 130) / 25
x = 3328 / 25
x ≈ 133.12 m²
To the nearest whole number, the area of the larger rectangle is approximately 133 m².