Question
The length of a rectangle is reduced by 20% and breadth
is kept constant, and the new figure that is formed is a square. Consider the following statements: 1. The area of the square is 25% less than the area of rectangle. 2. The perimeter of square is approximately 11% less than the perimeter of rectangle. 3. The diagonal of square is approximately 12% less than the diagonal of rectangle. Which of the statements given. above is/are correct?Solution
Let length of the rectangle = L, breadth of the rectangle = B Area= L*B Now, length reduced by 20%. So, now length – (4/5)L Breadth remains same So, new figure is square. So, (4/5)L = B So, New area = (4/5)L*B 1. Difference in area = [{L/B – (4/5) L*B}/ L*B]*100 = 20% (So, wrong as given in the statement 1 to be 25%) 2. Perimeter of square = 2(4/5) L + 2B = (8/5) L + 2B Perimeter of rectangle = 2(L + B) Difference = [{2L + 2B – (8/5)L – 2B}/ (2(L + B)]*100 = [(2/5)L/ 2(L + (4/5)L]*100 = 11.11% (So, right it is approx. 11%) 3. Diagonal of rectangle = √(L2 + B2) = √(L2 + (4/5 L)2 = (L/5)*√41 Diagonal of square =side*√2 = (4/5)L*√2 Require %age = [{(√41 - 4√2)*(L/5)}/(L/5)*√41]*100 = 11.65% (So, right it is approx. 12%) Hence option D.
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