A room has floor size of $15 \times 6$ sq.cm. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

Floor size = $15 \times 6$ sq.cm

Let height of room be $h$ cm

Area of base and roof = $2(15 \times 6)$ = $2(90)$ = $180$ sq.cm

Area of walls:

• Front and back walls = $2(15 \times h)$ = $30h$ sq.cm
  • Side walls = $2(6 \times h)$ = $12h$ sq.cm
  • Total wall area = $30h + 12h$ = $42h$ sq.cm

Given that sum of base and roof area = sum of wall areas:

$180 = 42h$

$h = \frac{180}{42}$

$h = 4.29$ cm

Therefore, the height of the room is $4.29$ cm.