Finding area using ratios

Question

 

 A                                   E                     B

 

 D                                      F                      C     

 

In the above diagram, ADFE is a square and ABCD is a rectangle.  The perimeter of ABCD is 132 and

 EB :AB =3:7.

Find the length of AE

Find the ratio of the area of rectangle EBCF to the area of rectangle ABCD is simplest form.

Answer 1

EB :AB =3:7

AE:EB=4:3

Let AE=4x=AD=width

AB=7x=length

2(l+w)=132

2(7x+4x)=132

11x=132/2=66

x=66/11=6

AE=4x=4*6=24 units

 area of rectangle EBCF / area of rectangle ABCD =18*24/42*24=3/7