Solution
For this case we know that:
P= 20 in represents the perimeter
A= 24 in^2 represent the area
We also know that by definition:
P= 2W+ 2H
A= W*h
Where W= width and H= height
So we have this:
20 = 2(W+H) (1)
24= WH (2)
Solving W from the (2) equation we got:
W= 24/H
Replacing into the first equation we got:
20 = 2 (W+H)
10= W+H= 24/H + H
10 = (24+H^2)/H
10H= 24 +H^2
H^2 -10H +24=0
(H-6)(H-4)=0
Then H= 4in or H=6in
Solving for W we got:
W= 24/4 = 6in, W= 24/6=4in
Then the dimensions are:
6 in and 4 in