A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeownercannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally.
I let x = different values but the same for the width and length.
If x = 12, then width = 12 + 15 = 27 ft.
If x = 12, then length = 12 + 20 = 32 ft.
The 32 ft times 27 ft = 864 ft, which is close to 900 square feet but not over 900 square feet.
However, the answer is 12.6 not 12.
How do I get 12.6?
I have a doubt here. The question says "by the same amount". This phrase can be interpreted in two different ways:
(1) By same amount : same increment. Example, both increase by 10 ft
(2) By same amount : by same percentage. (The the answer differs)
If I consider interpretation (2),
Final_length = Initial_Length * %total_percentage
Final_width = Initial_width * %total_percentage
The %total_percentage =
Let %total_percentage = x
Final_width * Final_length 900
20x * 15x 900
Therefore increase in length = (1.73*20 -25)ft = 14.6, which is also a correct answer based on my reasoning.
You cannot work according to the answer, because in a test, you cannot anticipate the correct answer. You have to work for it.