Question

F and E are the points on sides AB and CD of the rectangle ABCD that AFCE is a rhombus. If AB=16, BC =12 then find the length of EF. If AB= a, BC= b then find the length of EF.​

Answer 1

answer:EF=15cm

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Answer 2

Length of EF = 15 cm where F and E are the points on sides AB and CD of the rectangle ABCD that AFCE is a rhombus.AB=16, BC =12

Step-by-step explanation:

let say AF = CE = AE = CF = x   ( all sides of rhombus are equal)

then BF = AB - AF = 16 - x

BC = 12

CF² = BF² + BC²

=> x² = (16-x)² + 12²

=> x² = 256 + x² - 32x + 144

=> 32x = 400

=> x = 12.5

BF = DE = 16-x = 16-12.5 = 3.5

Horizontal Distance between EF = 16 - 2*(3.5) = 9 cm

Vertical distance between EF = 12 cm  ( = BC)

EF² = 9² + 12²

=> EF² = 225

=> EF = 15 cm

Length of EF = 15 cm

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