Question

a square room is surrounded by a verandah of width 2m. Area of the verandah is 72 sq m. Find the area of the room​

Answer 1

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we know,

Area of total land - Area of square = Area of veranda

Let side of square be a

So side of total land = a + 4 ( Side of sq. + 2 * width of veranda)

So ( a + 4 )² - a² = 72

We know,

( x + y)² = x² + y² + 2xy

a² - a² + 16 + 8a = 72

16 + 8a = 72

8a = 72 - 16

a = 56 / 8

a = 7 = Side of square

So area of room= 7² m²

= 49 m²

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Answer 2

Answer:

121 sq. m

Step-by-step explanation:

Area of the room (a^2) = (A+4w^2/4w)^2

where, a=area of the room, A= area of the verandah, w= width of verandah

$72 +16 = 88 \\ 88 \div 8 = 11 \\ 11 {}^{2} = 121$