Question

ABCD is a rectangle such that $AC+AB=5AD$ and $AC-AD=8$, then the area of rectangle ABCD is

• A. $36$sq. units
• B. $50$. sq. units
• C. $60$ sq. units
• D. Cannot be found

Answer 1

Answer: (C)

$60$ sq. units

L=length & b=breadth
$\therefore \sqrt{L^2+b^2}+L=5b$ (i)
$\sqrt{L^2+b^2}-b=8$
$L^2=64+16b$ (ii)
Solving (i) & (ii) we get
$L^2+4L-96=0$
$\therefore L=12,b=5$
Arcat $=Lb=60$ sq.units