In the diagram, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate
MATHEMATICS
WAEC 2008
In the diagram, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus
- A. 34cm
- B. 52cm
- C. 56cm
- D. 96cm
Correct Answer: B. 52cm
Explanation
For a rhombus, all the sides are equal and diagonals bisect each other at 90o. Hence, the triangles formed are congruent: (under RHS).
Thus: \(\bar{PS}^2\) = 52 + 122
\(\bar{PS} = \sqrt{25 + 144}\)
= \(\sqrt{169}\)
\(\bar{PS}\) = 13cm
perimeter = 4 x length of a side
= 4 x 13cm
= 52cm
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