Question 19

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waecmaths question: 

In the diagram PQRS is a rhombus$\left| PR \right|=10cm\text{ and }\left| QS \right|=24cm$. Calculate the perimeter of the rhombus.

Option A: 

34cm 

Option B: 

52cm

Option C: 

56cm

Option D: 

96cm

waecmaths solution: 

\[\begin{align}  & \text{The diagonals intersect at 9}{{\text{0}}^{\circ }}\text{ and also bisect each other} \\ & \left| OS \right|=\left| OQ \right|=12cm \\ & \left| OP \right|=\left| OR \right|=5cm \\ & \left| PS \right|=\sqrt{{{12}^{2}}+{{5}^{2}}}=13 \\ & \text{All the sides of a Rhombus are equal} \\ & \text{Therefore the perimeter is }13cm\times 4=52cm \\\end{align}\]

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