Question

Challenge Yael used to have a square garage with 370 ft ^2of floor space. She 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?
ft long
One side of the garage was originally
(Round to the nearest tenth as needed.)

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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