Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave your answer in surd form)

A.
8√3cm^{2} 
B.
12√3cm^{2} 
C.
16√2cm^{2} 
D.
16√3cm^{2}
Correct Answer: Option D
Explanation
AB = 4cm
BC = 8cm
In rightangled BAC; BC^{2}= AB^{2}+ AC^{2}
8^{2}= 4^{2}+ AC^{2}
64 – 16 = AC^{2}
48 = AC^{2}
(AC= sqrt{48}cm = 4sqrt{3}cm)
The area of rectangle = L x B = AB x AC
= ((4 times 4sqrt{3}cm^2)\
=16sqrt{3}cm^2)