Find the sum of areas of floor and ceiling of a room with the dimensions 144xy and 1/4 x ^3y^2
Answers
Given :-
- Dimensions of room are 144xy and (1/4)x³y².
To Find :-
- the sum of areas of floor and ceiling of a room ?
Solution :-
→ Length of room = 144xy
→ Breadth of room = (1/4) x³y² .
So,
→ Area of floor = Length * Breadth
Putting values we get :-
→ Area of floor = (144xy) * {(1/4)x³y²}
→ Area of floor = (144/4) * (xy) * (x³y²)
→ Area of floor = 36 * (x)^(1 + 3) * (y)^(1 + 2) . { using a^b * a^c = a^(b + c) }
→ Area of floor = 36x⁴y³ Sq. units.
Now, we know that, area dimensions of a floor is Equal to dimensions of a ceiling of a room.
Therefore, area of floor is equal to area of ceiling of a room.
Hence,
→ Area of floor + Area of ceiling
→ Area of floor + Area of floor
→ 2(Area of floor)
→ 2(36x⁴y³)
→ 72x⁴y³ Sq. units. (Ans.)
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