Question

ABCD is a rectangle with AB = 16units and BC = 12units. F is a point on
AB and E is a point on CD such that AFCE is a rhombus. Then, EF is​

Answer 1

Answer:

As AECF is a rhombus, AE = EC = CF = AF -------(1)

In triangle EBC,

EC2 = BE2 + BC2

or AE2 = (16 - AE)2 + 122

or AE2 = 256 + AE2 - 32AE + 144

or 32AE = 400

or AE = 400 / 32 = 12.5 units

area of rhombus = AE * BC //as BC is the height for base AE

= 12.5 * 12 = 150 sq. units

Also, area of rhombus = 1/2 * EF * AC //1/2 * diagonal 1 * diagonal 2

or 1/2 * EF * 20 = 150 //AC2 = AB2 + BC2 or AC2= 162 + 122 = 256 + 144 = 400 or AC = root 400 = 20

or 10 * EF = 150

or EF = 150 / 10 = 15 units

Answer 2

AC² = 256+144 = 400

AC = square root of 400 = 20