Find the area of a rectangle of length 4cm and whose diagonal is 8cm, (Leave your answer in surd form)

A.

8√3cm2

B.

12√3cm2

C.

16√2cm2

D.

16√3cm2

Correct answer is D

|AB| = 4cm
|BC| = 8cm
In right-angled BAC;

8\(^2\) = 4\(^2\) + |AC|\(^2\)

|AC|\(^2\) = 8\(^2\) - 4\(^2\)

|AC\\(^2\) = 64 - 16 → 48

|AC| = \(\sqrt{48}\)cm → \(4\sqrt{3}cm\)

The area of rectangle = L x B

= |AB| x |AC|
= \((4 \times 4\sqrt{3}cm^2\)
=\(16\sqrt{3}cm^2\)