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Yossi used to have a square garage with 250 ft 2 of floor space. He recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?



Answer :

sqdancefan

Answer:

  • 5√10 ≈ 15.81 ft
  • 5√15 ≈ 19.36 ft
  • 22.47%

Step-by-step explanation:

You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.

Side length

The area of a square is given by the formula ...

  A = s²

Solving for the side length (s), we find ...

  s = √A

The side length of a square with 250 ft² area is ...

  s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length

The area of a square that has 50% more area is ...

  (250 ft²) × (1 +50%) = 375 ft²

The side length of that square is ...

  √375 ft = 5√15 ft ≈ 19.36 ft . . . side length

Percentage change

The percentage change can be found from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%

The percentage increase in the length of one side is about 22.47%.

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