Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
2 : 5
4 : 9
3 : 8
1 : 3
Answers
Answer:
The correct option is D
Explanation:
Let the area of square ABCD be 100.
Side of ABCD = 10
Area of EFGH = 62.5
Side of EFGH = √62.5
Triangles AEH, BFE, CGF and DHG are congruent by ASA.
Let AE = BF = CG = DH = x
EB = FC = DG = AH = 10 - x
AE2 + AH2 = EH2
x2 + (10 - x)2 = (√62.5)2
Solving,
x = 2.5 or 7.5
Since, CG is longer than EB,
CG = 7.5 and EB = 2.5
Therefore, EB : CG = 1 : 3
Answer:
The correct option is D
Explanation:
Let the area of square ABCD be 100.
Side of ABCD = 10
Area of EFGH = 62.5
Side of EFGH = √62.5
Triangles AEH, BFE, CGF and DHG are congruent by ASA.
Let AE = BF = CG = DH = x
EB = FC = DG = AH = 10 - x
AE2 + AH2 = EH2
x2 + (10 - x)2 = (√62.5)2
Solving,
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Explanation: