Question

The length breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then total area of the four walls of the room will (1) Remain the same (2) Decrease by 30% (3) Decrease by 15% (4) Decrease by 18.75%

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Answer 1

Answer:

option 2 is correct

Step-by-step explanation:

Let length, breadth and height of the room be 3, 2, 1 unit respectively.

Area of walls = 2(l + b) × h = 2(3 + 2) × 1 = 10 sq. unit.

Now, length, breadth and height of room will become 6, 1 and 12

respectively.

Now, area of walls = 2(6+1)×12

= 7 sq. unit.

% decrease in the area of walls = (10−7)×10010

= 30%

Answer 2

SOLUTION :-

$\longrightarrow$Let us consider the room with,

$\longrightarrow$Length (l) = 3x

$\longrightarrow$Breadth (b) = 2x

$\longrightarrow$Height (h) = 1x

$\longrightarrow$Area of the walls (A) = 2(l + b) × h

$\longrightarrow$A = 2(3x + 2x) × 1x

$\longrightarrow$A = 10x² sq. unit.

$\longrightarrow$Now,

$\longrightarrow$ $l {}^{1}$ = 6x

$\longrightarrow$ $b {}^{1}$ = x

$\longrightarrow$ $h {}^{1}$ = $\frac{x}{2}$

$\longrightarrow$ New area =$(A^1)$ = 2(6x + x) (x/2)

$\longrightarrow$ $(A^1)$= 7x² sq. unit

$\longrightarrow$ % decrease in the area of walls = 30% .