#### Answer

$x = 9$ ft
$y = 7.5$ ft
The perimeter of the large triangle is $22.5$ ft.

#### Work Step by Step

1. Using the small triangle, find the ratios between the lengths
a) Ratio between $4$ ft and $6$ ft (Large triangle: $6$ ft and $x$)
$4a=6$
$a = 1.5$
b) Ratio between $4$ ft and $5$ ft (Large triangle: $6$ ft and $y$)
$4a=5$
$a=1.25$
2. Use the ratios to find $x$ and $y$
a) Finding $x$
$x=6 × 1.5$
$x=9$ ft
b) Finding $y$
$y=6×1.25$
$y=7.5$ ft
Currently, the lengths in the large triangle are $6$ ft, $7.5$ ft and $9$ ft.
3. Find the perimeter of the large triangle
Let $P=$ perimeter of the large triangle
$P=6 + 7.5 + 9$
$P= 15 + 7.5$
$P = 22.5$ ft
Therefore the perimeter of the large triangle is $22.5$ ft.