Answer:
A = 1/2 width × height
width = n + 3 cm
height = width - 9 cm
height = n + 3cm - 9cm
height = n - 6cm
A = 1/2 width × height
= 1/2 (n + 3cm) × (n - 6cm)
45cm^2 ×2 = n^2 - 3ncm - 18cm^2
n^2 - 3ncm - 18cm^2 - 90cm^2 = 0
n^2 - 3ncm - 108cm^2 = 0
Find two numbers that their sum is -3 and their product is 108. Therefore, the numbers could be -12 and 9
n^2 - 3ncm - 108cm^2 = 0
n^2 - 12ncm + 9ncm - 108cm^2 = 0
n(n - 12cm) + 9cm(n - 12cm) = 0
(n - 12cm) (n + 9cm) = 0
Either (n - 12cm) = 0 or (n + 9cm) = 0
n = 12cm or n = -9cm
but n = -9cm is invalid because there is no negative distance.
n = 12cm is the answer