Answer: base = 12 cm
Height = 7 cm
Explanation:
Let b represent the base of the rectangle.
Let h represent the height of the rectangle.
The base of a rectangle is 5 cm more than its height. It means that
b = h + 5
if we reduce the height by 2cm the area of the new rectangle is 60 cm square. It means that
b(h - 2) = 60- - - - - - - - -1
Substituting b = h + 5 into equation 1, it becomes
(h + 5)(h - 2) = 60
h² - 2h + 5h - 10 = 60
h² + 3h - 10 - 60 = 0
h² + 3h - 70 = 0
h² + 10h - 7h - 70 = 0
h(h + 10) - 7(h + 10)
h - 7 = 0 or h + 10 = 0
h = 7 or h = - 10
Since the height cannot be negative, then
h = 7 cm
b = h + 5 = 7 + 5
b = 12 cm