Question

A Verandah of area 90 m\(^2\) is around a room of length 15 m and breadth 12 m. The width of the verandah is:

• A. 1.5 m
• B. 2 m
• C. 2.5 m
• D. 1 m

Hint:

When calculating areas involving a verandah, subtract the area of the room from the total area of the outer rectangle to find the area of the verandah.

Answer 1

The Correct Option is B

The verandah's area is 90 m\(^2\). The room has a length of 15 m and a breadth of 12 m. Let \( x \) be the verandah's width in meters. The outer rectangle (room + verandah) has dimensions \( (15 + 2x) \) and \( (12 + 2x) \). Its area is: \[ \text{Area of outer rectangle} = (15 + 2x)(12 + 2x) \] The room's area is \( 15 \times 12 = 180 \) m\(^2\). The verandah's area is the outer rectangle's area minus the room's area: \[ \text{Area of verandah} = (15 + 2x)(12 + 2x) - 180 = 90 \] Simplifying: \[ (15 + 2x)(12 + 2x) = 270 \] Expanding and solving: \[ 180 + 54x + 4x^2 = 270 \] \[ 4x^2 + 54x - 90 = 0 \] Dividing by 2: \[ 2x^2 + 27x - 45 = 0 \] Using the quadratic formula: \[ x = \frac{-27 \pm \sqrt{27^2 - 4 \times 2 \times (-45)}}{2 \times 2} \] \[ x = \frac{-27 \pm \sqrt{729 + 360}}{4} = \frac{-27 \pm \sqrt{1089}}{4} \] \[ x = \frac{-27 \pm 33}{4} \] Therefore, \( x = \frac{6}{4} = 1.5 \) or \( x = \frac{-60}{4} = -15 \) (which is not valid). Thus, the verandah's width is \( 1.5 \) m.