waecmaths question:
The diagonal of a square is 60cm. Calculate its perimeter.
Option A:
$20\sqrt{2}$
Option B:
$40\sqrt{2}$
Option C:
$90\sqrt{2}$
Option D:
$120\sqrt{2}$
waecmaths solution:
$\begin{align} & \text{Since all the sides of a square are equal, that is} \\ & AB=BC=CD=DA \\ & \text{Let }AB=BC=CD=DA=x \\ & \text{Using pythagoras theorem} \\ & B{{D}^{2}}=D{{C}^{2}}+C{{B}^{2}} \\ & {{60}^{2}}={{x}^{2}}+{{x}^{2}} \\ & 3600=2{{x}^{2}} \\ & 1800={{x}^{2}} \\ & x=\sqrt{1800}=30\sqrt{2}cm \\ & \text{The perimeter of the square }=4x=4\times 30\sqrt{2}cm=120\sqrt{2}cm \\\end{align}$
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