Let the length be x and width be y
The perimeter is 42cm
2x + 2y = 42
The area is 80cm²
xy = 80
Rewrite the two equation here ...
2x + 2y = 42 ---------- (1)
xy = 80 ----------------- (2)
From (2):
xy = 80
x = 80/y ------- Sub into (1)
2(80/y) + 2y = 42
160/y + 2y = 42
Divide by 2 for every term
80/y + y = 21
multiply by y for every term
80 + y² = 21y
rearrange
y²-21y+80 = 0
(y - 16)(y - 5) = 0
y = 16 or y = 5 --------- sub into (2)
if y = 16
x(16) = 80
x = 5
if y = 5
x(5) = 80
x = 16
So the dimension are 16 cm and 5 cm
