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I have another 3 questions regarding Geometry which I suck at. Please help.?
I have another 3 questions regarding Geometry which I suck at. Please help.?
1) A rectangular rug 12 feet long and 8 feet wide is placed in a room such that all four sides of the rug are 2 feet away from the walls. What percent of the room is covered by the rug? (the answer is 50% but I don't understand why)
2) If the length of the diagonal of a rectangle is 10, and the perimeter of the rectangle is 24. Then was is the area of the rectangle? Please explain your answer
3) The area of Circle A is twice the area of Circle B. What is the ratio of the circumference of Circle A to that of Circle B? I think i am getting mixed up on the calucaltions (the answer is root 2:1) Please explain your answer
Answers:
Tony B: 2. Perimeter = 2L+2W, L=10
24=2(10)+2(W)
W=2
Area=L*W=10*2=20
2008-04-26 12:40:56
24=2(10)+2(W)
W=2
Area=L*W=10*2=20
2008-04-26 12:40:56
Justine L.: (1) The area of the room is: (12+2+2) x (8+2+2)= 192. The coverage of the rug is 12 x 8 = 96
% = 96 / 192 = 50%
(2) Suppose length=x, width=y
2 (x+y) = 24 x^2 + y^2 = 100 solve both equations, and you'll get the values of length and width
(3) Area of A= "pie" R^2
Area of B = "pie" r^2
Area of A = 2 Area of B
so, R^2 = 2 r^2
R / r = squared 2
Circumference of A = 2 "pie" R = 2 "pie" r x squared 2
C of B = 2 "pie" r
Therefore, C A / C B = squared 2 / 1
2008-04-26 12:46:44
% = 96 / 192 = 50%
(2) Suppose length=x, width=y
2 (x+y) = 24 x^2 + y^2 = 100 solve both equations, and you'll get the values of length and width
(3) Area of A= "pie" R^2
Area of B = "pie" r^2
Area of A = 2 Area of B
so, R^2 = 2 r^2
R / r = squared 2
Circumference of A = 2 "pie" R = 2 "pie" r x squared 2
C of B = 2 "pie" r
Therefore, C A / C B = squared 2 / 1
2008-04-26 12:46:44
Chosen Answer
richardwptljc: 1) The area of the rug is 12(8) = 96
The length and width of the room is 12+2+2= 16 and 8+2+2 = 12. Area of room is 16(12) = 192
192 = 2(96)
3) The ratio of the areas of the circles is A^2:B^2
The ratio of the circumferences is A:B
Sq rt 2 to Sq rt 1 = sq rt 2: 1
2008-04-26 12:46:48
richardwptljc: 1) The area of the rug is 12(8) = 96
The length and width of the room is 12+2+2= 16 and 8+2+2 = 12. Area of room is 16(12) = 192
192 = 2(96)
3) The ratio of the areas of the circles is A^2:B^2
The ratio of the circumferences is A:B
Sq rt 2 to Sq rt 1 = sq rt 2: 1
2008-04-26 12:46:48
John H: These sound like homework questions, but remember you can break a rectangle into two right triangles
then use side "a" squared plus side "b" squared is equal to the diagonal "c" squared. from there just divide to get the ratio.
use sohcahtoa [ sin = opposite over hypotenuse;
cosine = adjacent over hypotenuse and tangent is opposite over adjacent] for 2),
finally, on 3 just divide the two areas, the area of a circle is pi times the radius squared.
2008-04-26 12:49:39
then use side "a" squared plus side "b" squared is equal to the diagonal "c" squared. from there just divide to get the ratio.
use sohcahtoa [ sin = opposite over hypotenuse;
cosine = adjacent over hypotenuse and tangent is opposite over adjacent] for 2),
finally, on 3 just divide the two areas, the area of a circle is pi times the radius squared.
2008-04-26 12:49:39
ironduke8159: The dimensions of the room must be 16 by 12
The rug is 12*8
12*8/12*16 = 1/2 = 50%
2l+2w = 24 so l+w = 12
sqrt(l^2+w^2) = 10
l^2+w^2 = 100
(12-w )^2 +w^2 = 100
144 -24w +w^2 +w^2 = 100
2w^2 -24w +44 = 0
w^2 -12w +22 = 0
w = [12 +/- sqrt(56)]/2
w = 6 +/- sqrt(14)
You should be able to complete this now.
area circle A = pir1^2
area circle B = pir2^2
A/B = 2 = r1^2/r2^2
So r1/r2 = sqrt(2)
circumference of circle A = 2pir1
circumference of circle B = 2pir2
So A/B = r1/r2 = sqrt(2)
2008-04-26 13:03:49
The rug is 12*8
12*8/12*16 = 1/2 = 50%
2l+2w = 24 so l+w = 12
sqrt(l^2+w^2) = 10
l^2+w^2 = 100
(12-w )^2 +w^2 = 100
144 -24w +w^2 +w^2 = 100
2w^2 -24w +44 = 0
w^2 -12w +22 = 0
w = [12 +/- sqrt(56)]/2
w = 6 +/- sqrt(14)
You should be able to complete this now.
area circle A = pir1^2
area circle B = pir2^2
A/B = 2 = r1^2/r2^2
So r1/r2 = sqrt(2)
circumference of circle A = 2pir1
circumference of circle B = 2pir2
So A/B = r1/r2 = sqrt(2)
2008-04-26 13:03:49