A square with side lengths $z$ was cut from a rectangle to form the polygon as shown here.
Which expression represents the perimeter of the polygon ?

2 x + 4 y + 2 z

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2 x + 4 y + 3 z

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2 x + 4 y + 4 z

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2 x + 4 y + 6 z

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Solution

The correct option is D $2 x + 4 y + 4 z$
perimeter of the polygon= perimeter of rectangle+perimeter of the square-common sides
$P = 2 (x + 2 y + z) + 4 * z - 2 z$
$P = 2 x + 4 y + 4 z$
Answer (C) $2 x + 4 y + 4 z$

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2^{x} = 4^{y} = 8^{z}

(\frac{1}{2 x} + \frac{1}{4 y} + \frac{1}{6 z}) = \frac{24}{7}

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