# A pathway is constructed around a garden whose length is 15 yards and width is 12 yards. If the total area is 340 sq yards, how do you find the length, width and area of the pathway?

Jan 18, 2018

area: $160$ sq yd
length: $20.6$ yd
width: $16.5$ yd

#### Explanation:

total area = area of garden + area of pathway

$340 = \left(15 \cdot 12\right) +$ area of pathway

$= 340 - 180 = 160$

area of pathway $= 160$ sq yd

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total area $= 340$ sq yd

the pathway is constructed around the garden.
its dimensions (length and width) must be similar (directly proportional) to the dimensions of the field.

$l = 15$
$w = 12$

the area found by multiplying the length and width of the pathway is the same as the total area, $340$ sq yd.

$\frac{340}{180} = \frac{17}{9}$
(ratio of area of field to total area)

$\sqrt{\frac{17}{9}} = \frac{\sqrt{17}}{3}$
(ratio of lengths)

$15 \cdot \frac{\sqrt{17}}{3} = 5 \left(\sqrt{17}\right) = 20.6$ (3s.f.)

$12 \cdot \frac{\sqrt{17}}{3} = 4 \left(\sqrt{17}\right) = 16.5$ (3s.f.)

dimensions of the pathway:

$l = 20.6$ yd
$w = 16.5$ yd

to check:
$l w = 339.9 \approx 340$
$340 =$ total area