SOLUTION: A building is constructed on a rectangular plot 3 times as long as it is wide. The building needed expanding a few years later. A portion of land containing 77 sq. yds. was obtai

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Question 1205909: A building is constructed on a rectangular plot 3 times as long as it is wide. The building needed expanding a few years later. A portion of land containing 77 sq. yds. was obtained, increasing the lot 3 ft. in each direction. Determine dimensions of new plot.
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Answer by math_helper(2461) About Me  (Show Source):
Answer by math_tutor2020(3816) About Me  (Show Source):
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x = original width in yards
3x = original length in yards
length*width = 3x*x = 3x^2 = original area in square yards


3 ft = 1 yard
We're adding two copies of 1 yard to each dimension, i.e. 2 yards.
Draw out a picture similar to what is shown here


x becomes x+2
3x becomes 3x+2

new area = (x+2)(3x+2) = 3x^2+8x+4 due to the FOIL rule

Subtract the new and old areas to find the amount of area gained
new - old = (3x^2+8x+4) - (3x^2) = 8x+4

Set this equal to the 77 square yards gained.
8x+4 = 77
8x = 77-4
8x = 73
x = 73/8
x = 9.125 is the original width in yards.

And 3x = 3*9.125 = 27.375 yards is the original length.

The original plot of land was 9.125 yards by 27.375 yards.

Add 2 to each result to get the new dimensions.
9.125+2 = 11.125
27.375+2 = 29.375

The dimensions of the new plot of land are 11.125 yards by 29.375 yards

Side notes:
11.125 = 11 & 1/8
29.375 = 29 & 3/8