Q1 of 53 Page 156

In rectangle ABCD, AB + BC = 23, AC + BD = 34. Find the area of the rectangle.

AB + BC = 23


AC + BD = 34


Since Diagonals of a rectangle are of equal length, so


AC = BD = 17


Let AB be x, BC = 23 – x


Applying Pythagoras theorem :


x2 + (23 – x)2 = 172


⇒ 2x2 – 46x + 240 = 0


⇒ x2 – 23x + 120 = 0


⇒ x2 – 15x – 8x + 120 = 0


⇒ x(x – 15) – 8(x – 15) = 0


⇒ (x – 8)(x – 15) = 0


x = 8, 15


∴ The two sides are 8 and 15


Area of the Rectangle = (8 × 15) = 120 sq. units


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