Question : The perimeter of a rectangle is 68 cm. If the area of the rectangle is 240 cm2, then what is the length of each of its diagonals?
Option 1: 25 cm
Option 2: 27 cm
Option 3: 26 cm
Option 4: 28 cm
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Correct Answer: 26 cm
Solution : Given, Perimeter of a rectangle = 68 cm Area of the rectangle = 240 cm 2 Let the length be l and breadth be b. Perimeter of Rectangle = 2(l + b) ⇒ 2(l + b) = 68 ⇒ l + b = 34............(1) Also, Area of rectangle = l × b ⇒ l × b = 240.............(2) From (1), we get l = 34 – b, ⇒ (34 – b) × b = 240 ⇒ b 2 – 34b + 240 = 0 ⇒ b 2 – 10b – 24b + 240 = 0 ⇒ b(b – 10) – 24(b – 10) = 0 ⇒ (b – 24)(b – 10) = 0 ⇒ b = 10 or 24 $\therefore$ Length, l = 24 or 10 cm We know, Pythagoras's theorem: Perpendicular 2 = Length 2 + Breadth 2 ⇒ Length of diagonal = $\sqrt{24^2+10^2}=\sqrt{576+100}=\sqrt{676}= 26\ \text{cm}$ Hence, the correct answer is 26 cm.
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