Question

Challenge Yael used to have a square garage with 370 ft ^2of floor space. She recently built an

Answer 1

Scale factor of area is the square of the scale factor of length

The required values are;

• The length of one sides of the garage was originally approximately 19.2 ft.

• The length of one of the sides of the garage is now approximately 23.6 feet long

• The percentage increase in length is approximately 22.5 %

Reason:

The given parameters are;

The area of the square garage = 370 ft.²

The area of the new garage has 50% more space

Required;

Part A

The initial side length

The initial side length, given to the nearest tenth, s, is the square root of the area, A, given as follows;

• s = √(370 ft.²) ≈ 19.2 ft.

Part B

The side was increased by 50%, to give,

370 + 0.5×370 = 555

The new area of the garage = 555 ft.²

The side length of the new garage, s = √(555) ≈ 23.6

• The side of the garage now is 23.6 ft.

Part C

The percentage increase is given as follows;

$The \ percentage \ increase \ in \ length = \dfrac{New \ length - Initial \ length}{Initial \ length }$

$The \ percentage \ increase \ in \ length = \dfrac{\sqrt{555} - \sqrt{370} }{\sqrt{370} } \times 100 \approx 22.5 \%$

• The percentage increase in length of the side of the garage is approximately 22.5 %

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