Question : A rectangular LCD has an area of 480 cm²and a perimeter of 92 cm. If the size of the LCD is defined in terms of the length of the diagonal, then what is the size of the LCD?
Option 1: 34 cm

Option 2: 39 cm
Option 3: 31 cm
Option 4: 35 cm

Question

Question : A rectangular LCD has an area of 480 cm²and a perimeter of 92 cm. If the size of the LCD is defined in terms of the length of the diagonal, then what is the size of the LCD?

Option 1: 34 cm

Option 2: 39 cm

Option 3: 31 cm

Option 4: 35 cm

Team Careers360 · Accepted Answer

Correct Answer: 34 cm

Solution : The perimeter of a rectangular LCD is = 92 cm
Area is = 480 cm$^2$
Let the length = l and breadth = b
Then, 2(l + b) = 92
⇒ l + b = 46 … (1)
And lb = 480 ….(2)
Now (l – b)$^2$ = (l + b)$^2$ - 4lb
⇒ (l – b)$^2$ = 2116 - 4 × 480
⇒ (l – b)$^2$ = 2116 - 1920 = 196
⇒ l – b = 14 ….(3)
By adding, equations (1) and (3)
⇒ 2l = 60
⇒ l = 30 cm
⇒ b = 16 cm
Then, (Diagonal)$^2$ = 30² + 16²
⇒ (Diagonals)$^2$ = 1156
⇒ Diagonals = 34 cm
Hence, the correct answer is 34 cm.

Popular Searches

Question : A rectangular LCD has an area of 480 cm²and a perimeter of 92 cm. If the size of the LCD is defined in terms of the length of the diagonal, then what is the size of the LCD?
Option 1: 34 cm

Option 2: 39 cm
Option 3: 31 cm
Option 4: 35 cm

Related Questions

Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm²
Option 2: 265 cm²
Option 3: 315 cm²
Option 4: 351 cm²

Question : 5 times the perimeter of a square is 600 cm. What will be the area of this square?
Option 1: 900 cm²
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Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
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Popular Searches

Question : A rectangular LCD has an area of 480 cm2 and a perimeter of 92 cm. If the size of the LCD is defined in terms of the length of the diagonal, then what is the size of the LCD?Option 1: 34 cm Option 2: 39 cmOption 3: 31 cmOption 4: 35 cm

Related Questions

Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:Option 1: 256 cm2Option 2: 265 cm2Option 3: 315 cm2Option 4: 351 cm2

Question : 5 times the perimeter of a square is 600 cm. What will be the area of this square?Option 1: 900 cm2Option 2: 1150 cm2Option 3: 750 cm2Option 4: 480 cm2

Question : The length of each diagonal of a rectangle is 50 cm. If its breadth is 14 cm, then what will be the area of the rectangle?Option 1: 832 cm2Option 2: 716 cm2Option 3: 784 cm2Option 4: 672 cm2

Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?Option 1: 128 cm2Option 2: 112 cm2Option 3: 184 cm2Option 4: 156 cm2

Question : What is the area of a square whose diagonal is $5 \sqrt{2}$ cm?Option 1: 64 cm2Option 2: 25 cm2Option 3: 100 cm2Option 4: 36 cm2