The length of a rectangle is $3 x - 4 y + 6 z$ and its perimeter is $8 x + 9 y + 18 z$ . Breadth of the rectangle is

(x + 172 y + 3 z)

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(12 x + 8 y + 52 z)

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(x + 12 y + 6 z)

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(x + 17 y + 3 z)

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Solution

The correct option is A $(x + 172 y + 3 z)$
Let the breadth be b.
Length (l) $= 3 x - 4 y + 6 z$
Perimeter (P) $= 8 x + 9 y + 18 z$
$\Rightarrow P = 2 (l + b)$
$\Rightarrow 8 x + 9 y + 18 z = 2 (3 x - 4 y + 6 z + b)$
$\Rightarrow 8 x + 9 y + 18 z = 6 x - 8 y + 12 z + 2 b$
$\Rightarrow 2 b = (8 x + 9 y + 18 z) - (6 x - 8 y + 12 z))$
$\Rightarrow 2 b = (8 x + 9 y + 18 z) - (6 x - 8 y + 12 z)$
$\Rightarrow 2 b = (8 x + 9 y + 18 z - 6 x + 8 y - 12 z)$
$\Rightarrow 2 b = (2 x + 17 y + 6 z)$
$\Rightarrow b = (x + \frac{17}{2} y + 3 z)$

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3 x - 4 y + 6 z

8 x + 9 y + 18 z

The length of a rectangle is $\frac{3 x}{4} + 1$ and its breadth is $\frac{2 x}{3} - 1$ . If its perimeter is $34$ units. Find $x .$

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