SOLUTION: If each dimension of a rectangle were increased by 5 feet, the area would be increased by 95 feet and one dimension would become twice the other. Find the original dimensions.
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Question 122623: If each dimension of a rectangle were increased by 5 feet, the area would be increased by 95 feet and one dimension would become twice the other. Find the original dimensions. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! If each dimension of a rectangle were increased by 5 feet, the area would be increased by 95 feet and one dimension would become twice the other. Find the original dimensions.
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Let the original dimensions of the rectangle = x and y; where x is the length
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"If each dimension of a rectangle were increased by 5 feet, the area would be increased by 95 feet"
write an equation for this:
(x+5)*(y+5) = xy + 95
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"one dimension would become twice the other." write this as:
(x+5) = 2(y+5)
x + 5 = 2y + 10
x = 2y + 10 - 5
x = 2y + 5
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In the first equation substitute (2y+5) for x
(x+5)*(y+5) = xy + 95
((2y+5)+5) * (y+5) = y(2y+5) + 95
:
(2y + 10)(y + 5) = 2y^2 + 5y + 95
FOIL
2y^2 + 20y + 50 = 2y^2 + 5y + 95
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Combine the y's on the left, numerical values on the right
2y^2 - 2y^2 + 20y - 5y = 95 - 50
:
15y = 45
y =
y = 3 ft is the original width
Find x
x = 2y + 5
x = 2(3) + 5
x = 11 ft is the original length
:
:
Check it by comparing the areas:
Added 5' area = 8*16 = 128 sq/ft
Original area = 3*11 = 33 sq/ft
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difference between ares:95 sq/t
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Did this make sense to you? Any questions?
