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
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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