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zel117
24.04.2020 •
Mathematics
The length of a rectangle is 4 ft. greater than the width. If each dimension is increased by 3,
the new area will be 45 square feet. Find the dimensions of the original rectangle.
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Ответ:
Step-by-step explanation:
Original rectangle:
Let width = x ft
Length = x + 4
New rectangle
length = x + 4 + 3 = x +7
Width = x + 3
Area = 45 sq. ft
length * width = 45
(x + 7)(x + 3) = 45
Use FOIL method
x*x + x*3 + 7*x + 7*3 = 45
x² + 3x + 7x + 21 = 45
x² + 10x + 21 - 45 = 0
x² + 10x - 24 = 0
x² + 12x - 2x - 12*2 = 0
x*(x + 12) - 2*(x + 12) = 0
(x + 12)(x - 2) = 0
x - 2 = 0
x = 2 {x +12 is ignored because measurement cannot have negative value}
Dimensions of the original rectangle:
Width = 2 ft
Length = 2 + 4 = 6 ft
Ответ: