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In two Equilateral parallelograms, A and B, the sum of the..
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23 Oct 2020, 20:40
23 Oct 2020, 20:40
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29% (03:35) correct
70% (02:45) wrong based on 62 sessions
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In two Equilateral parallelograms, A and B, the sum of the lengths of the diagonals of A is equal to the sum of the lengths of the diagonals of B. In A, the length of the longer diagonal is 20 more than the length of the shorter diagonal. In B, the length of the longer diagonal is 8 more than the length of the shorter diagonal. What is the area of B minus the area of A?
A. 336
B. 168
C. 84
D. 42
E. 0
A. 336
B. 168
C. 84
D. 42
E. 0
Re: In two Equilateral parallelograms, A and B, the sum of the..
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24 Oct 2020, 07:36
24 Oct 2020, 07:36
5
Is there a better and faster way to solve this? It seems pretty hard to me. Here is I how I solve it:
Call XA and YA the diagonals of the parallelogram A, and XB and YB the diagonals of the parallelogram B. We have
(1) XA+YA=XB+YB.
(2) XA=YA+20.
(3) XB=YB+8.
Since the parallelograms are equilateral, the diagonals intersect with a 90º angle. Therefore, the area of the parallelograms are given by:
A: \(XA*YA/2=YA*(YA+20)/2=(YA^2+20YA)/2\)
B: \(XB*YB/2=YB(YB+8)/2=(YB^2+8YB)/2\)
B-A : \((YB^2+8YB-(YA^2+20YA))/2\)
Substitute (2) and (3) in (1). This gives you: 2YA+20=2YB+8.
Simplify: YA+10=YB+4. Square both sides:
\(YA^2+20YA+100=YB^2+8YB+16\)
This leads to \(YB^2+8YB-(YA^2+20YA)=84\). Dividing by two we have the difference between the two areas:
Answer is D
Call XA and YA the diagonals of the parallelogram A, and XB and YB the diagonals of the parallelogram B. We have
(1) XA+YA=XB+YB.
(2) XA=YA+20.
(3) XB=YB+8.
Since the parallelograms are equilateral, the diagonals intersect with a 90º angle. Therefore, the area of the parallelograms are given by:
A: \(XA*YA/2=YA*(YA+20)/2=(YA^2+20YA)/2\)
B: \(XB*YB/2=YB(YB+8)/2=(YB^2+8YB)/2\)
B-A : \((YB^2+8YB-(YA^2+20YA))/2\)
Substitute (2) and (3) in (1). This gives you: 2YA+20=2YB+8.
Simplify: YA+10=YB+4. Square both sides:
\(YA^2+20YA+100=YB^2+8YB+16\)
This leads to \(YB^2+8YB-(YA^2+20YA)=84\). Dividing by two we have the difference between the two areas:
Answer is D
General Discussion
Re: In two Equilateral parallelograms, A and B, the sum of the..
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24 Oct 2020, 02:20
24 Oct 2020, 02:20
Expert Reply
Please Sir provide the OAs when you do post a question. Please
Regards
Regards
