A rectangular LCD has an area of 480 CM2 and a perimeter of 92 cm If the size of the LCD is defined ...........

Quantitative Aptitude (MTS) Mensuration 2D

A rectangular LCD has an area of 480 CM² and a perimeter of 92 cm. If the size of the LCD is defined in term of length of the

diagonal, then what is the size of the LCD?

This questions was previously asked in

SSC MTS 12th July 2022 Shift-3

34 cm

39 cm

31 cm

35 cm

Let's break it down:

- Let the length = x cm and width = y cm.

- Area: x × y = 480 cm².

- Perimeter: 2(x + y) = 92 cm ? x + y = 46 cm.

- Using x + y = 46 and x × y = 480, create a quadratic: x² - 46x + 480 = 0.

- Solving:

x = [46 ± v(2116 - 1920)] / 2

x = [46 ± v196] / 2

x = [46 ± 14] / 2

So x = 30 cm or 16 cm.

- So dimensions are 30 cm and 16 cm.

- Diagonal: v(30² + 16²) = v(900 + 256) = v1156 = 34 cm.

So, the correct answer is option 1: 34 cm.

- Option 2 (39 cm), 3 (31 cm), and 4 (35 cm) are incorrect as they do not fit calculated values.

- Calculations match both area and perimeter, confirming the diagonal is 34 cm.

- The correct size of the LCD (length of the diagonal) is 34 cm.

- Hence, option 1 is correct.

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