Final answer:
The original side length of the square garage was approximately 17.2 feet. The new side length after the extension, which gave 50% more floor space, is approximately 21.07 feet. The percent increase in the length of the side is approximately 22.5%.
Step-by-step explanation:
To solve the original and current length of one side of the garage we will use the area of a square which is calculated by squaring the side length (s2). The original garage area is 296 ft2, thus the original side length (s) can be found by taking the square root of 296 ft2:
s = √296 = approximately 17.2 feet.
The new garage has 50% more floor space which means the new area is 296 ft2 plus 50% of 296 ft2:
New area = 296 ft2 + (0.5 × 296 ft2) = 444 ft2.
The new side length (s) can be calculated by taking the square root of 444 ft2:
s = √444 = approximately 21.07 feet.
To find the percent increase in the length of one side, we subtract the original side length from the new side length, divide by the original side length, and multiply by 100:
Percent increase = ((21.07 - 17.2) / 17.2) × 100 = approximately 22.5%.