#### Answer

$x = 34$ ft
$y = 30$ ft
The perimeter of the larger triangle is $104$ ft.

#### Work Step by Step

1. Using the small triangle, find the ratios between the lengths
a) Ratio between $20$ ft and $17$ ft (Large triangle: $40$ ft and $x$)
$20a = 17$
$a = 0.85$
b) Ratio between $20$ ft and $15$ ft (Large triangle: $40$ ft and $y$)
$20a = 15$
$a = 0.75$
2. Use the ratios to find $x$ and $y$
a) Finding $x$
$x = 40 \times 0.85$
$x = 34$ ft
b) Finding $y$
$y = 40 \times 0.75$
$y = 30$ ft
Currently, the lengths in the large triangle are $30$ ft, $34$ ft and $40$ ft.
3. Find the perimeter of the large triangle
Let $P =$ perimeter of the large triangle
$P = 30 + 34 + 40$
$P = 64 + 40$
$P = 104$ ft
Therefore the perimeter of the large triangle is $104$ ft.