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The area of the four walls of a room is 780 m2 and its length is twice its breadth. If the height of the room is 13m, then the area of its floor is equal to:
295 m²
150 m²
315 m²
200 m²
200 m²
Since l=2b, perimeter P=2(l+b)=2(2b+b)=6b. Wall area 780=P×h=6b×13. Thus, 6b=60, so b=10 and l=20. Area of floor = l×b=20×10=200.
Area of four walls = 780 m², Length (l) = 2 * Breadth (b), Height (h) = 13 m.
Areawalls=2h(l+b)
Since l=2b, perimeter P=2(l+b)=2(2b+b)=6b. Wall area 780=P×h=6b×13. Thus, 6b=60, so b=10 and l=20. Area of floor = l×b=20×10=200.
Students often use the surface area formula 2(lb+lh+bh) instead of the lateral surface area (four walls) formula 2h(l+b).
Define variables and formula
Let breadth be b meters. Given that length l=2b and height h=13 m. The area of the four walls is given by the formula 2h(l+b).
2h(l+b)=780
Substitute and solve for b
Substitute l=2b and h=13 into the equation: 2×13×(2b+b)=780. This simplifies to 26×3b=780, or 78b=780.
b=78780=10
Calculate length and area of the floor
With b=10, l=2×10=20. The area of the floor is l×b=20×10=200 m².
Areafloor=20×10=200
D is correct because the calculated area of the floor is 200 m².
This problem uses the lateral surface area of a cuboid; remember that in competitive exams, 'four walls' always refers to 2h(l+b) (excluding ceiling and floor).
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