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In rectangle ABCD, parallel lines k and m through A and C are perpendicular to diagonal BD and divide it into three equal segments of 1. What is the area of rectangle ABCD?

 Dec 5, 2021
 #1
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The square is a rectangle too !!! wink

 

If BD = 3 then [ABCD] = 4.5 square units laugh

 Dec 6, 2021
 #2
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AD = a          AB = b           BD = c

 

b = sqrt(9 - a2)            

 

AM = sqrt(a2 - 1)            (AM is the height of triangle ADM)

 

BD * AM = a * b

 

3[sqrt(a2 - 1)] = a[sqrt(9 - a2)]

 

a = √3          b = √6

 

[ABCD] = 3√2

jugoslav  Dec 6, 2021

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