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# Geometry Help

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Need some help with a few questions I was stuck on. Thanks!

1) Shown below is rectangle EFGH. Its diagonals meet at Y. Let X be the foot if an altitude is dropped from E to FH. If EX = 24 and GY = 25, find the perimeter of rectangle EFGH.

2) Which of the following statements are correct?

A. If one interior angle of a parallelogram is a right angle, then the parallelogram must be a rectangle.

B. If two diagonals of a rectangle are perpendicular, then the rectangle must be a square.

C. If two diagonals of a rhombus are equal, then the rhombus must be a square.

D. If one interior angle of a rhombus is a right angle, then the rhombus must be a square.

E. If two diagonals of a parallelogram are equal, then the parallelogram must be a rectangle.

I got A, B, C, D for this but it wasn't correct

Dec 30, 2019

#1
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1) The perimeter of EFGH is 125.

2) Only statements A, B, and D are true.

Dec 30, 2019
#2
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Those weren't right. Could you also explain a bit? Thanks

Guest Dec 30, 2019
#3
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I think #1 is 140

Guest Dec 31, 2019
#4
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EX = 24

GY = 25

XY = ?                        XY = sqrt [(EY)2 - (EX)2]          XY = 7

HX = ?                        HX = GY - XY                          HX = 18

EH = ?                        EH = sqrt [(EX)2 + (HX)2]         EH = 30

FH = ?                        FH = 2 * GY                             FH = 50

EF = ?                        EF = sqrt [(FH)2 - (EH)2]          EF = 40

Perimeter  P = 2*(EX) + 2*(EF)              P = 140 units

Dec 31, 2019