Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave...
MATHEMATICS
WAEC 2004
Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave your answer in surd form)
- A. 8√3cm2
- B. 12√3cm2
- C. 16√2cm2
- D. 16√3cm2
Correct Answer: D. 16√3cm2
Explanation
|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\)
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