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In Fig., if parallelogram ABCD and rectangle ABEF are of equal area, then :(A) Perimeter of ABCD = Perimeter of ABEM(B) Perimeter of ABCD < Perimeter of ABEM(C) Perimeter of ABCD > Perimeter of ABEM(D) Perimeter of ABCD = ½ (Perimeter of ABEM) |
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Answer» (C) Perimeter of ABCD > Perimeter of ABEM Explanation: In rectangle ABEM, AB = EM …(eq.1) [sides of rectangle] In parallelogram ABCD, CD = AB …(eq.2) Adding, equations (1) and (2), We get AB + CD = EM + AB …(i) We know that, Perpendicular distance between two parallel sides of a parallelogram is always less than the length of the other parallel sides. BE < BC and AM < AD [because, in a right angled triangle, the hypotenuse is greater than the other side] On adding both above inequalities, we get SE + AM <BC + AD or BC + AD> BE + AM On adding AB + CD both sides, we get AB + CD + BC + AD> AB + CD + BE + AM ⇒ AB+BC + CD + AD> AB+BE + EM+ AM [∴ CD = AB = EM] Hence, We get, Perimeter of parallelogram ABCD > perimeter of rectangle ABEM Hence, option (C) is the correct answer. |
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