InterviewSolution
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The two diagonals of a rhombus are of lengths 55 cm and 48 cm. If p is the perpendicular height of the rhombus, then which one of the following is correct?1). 36 cm < p < 37 cm2). 35 cm < p < 36 cm3). 34 cm < p < 35 cm4). 33 cm < p < 34 cm |
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Answer» Solution: Let us take ABCD as the rhombus with obtuse angle at D and B. Let us take E as the point where perpendicular from D MEETS AB and we know that DE is the perpendicular height of the rhombus. Let the two diagonals of the rhombus meet at the point O. We have two right angle triangles ∆AOB and ∆DEB. These two triangles are SIMILAR as they have the same angle B and the perpendicular of rhombus bisect each other at right angle. So,∆AOB ~ ∆DEB (so, their sides are PROPORTIONAL) AO/DE = AB/DB So, DE(perpendicular height) = AO × (DB/AB) It is given that DB= 48CM and AC=55cm so, AO= 55/2cm Using PYTHAGORAS theorem in ∆AOB we get, AB² = AO² + OB² AB² = (55/2)² + (48/2)² AB² = 27.5² + 24² AB² = 756.25 + 576 AB² = 1332.25 AB = √1332.25 AB = 36.5cm We know DE(p) = AO × (DB/AB) DE(p) = 27.5 × (48/36.5) DE(p) = 27.5 × 1.315 DE(p) = 36.15 cm So,the correct option is 1). 36 cm < p < 37 cm |
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