The perimeter of the shape shown below is given to be 100 units. Find $x .$

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Solution

The correct option is B
10

Perimeter of the figure $= (x + 2) + (x + 3) + (2 x + 2)$
$+ (2 x + 8) + x + (x + 5)$
Grouping the variables and numbers, we get
$(x + x + 2 x + 2 x + x + x) + (2 + 3 + 2 + 8 + 5) = (8 x + 20) .$

Given that the perimeter of the shape equals 100 units.
$∴ 8 x + 20 = 100$
Subtracting 20 from both sides of the equation, we get
$8 x + 20 - 20 = 100 - 20$
i.e., $8 x = 80$
Dividing both sides of the equation by 8, we get $x = \frac{80}{8} = 10.$
Thus, $x = 10$ units.

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