The base of a rectangle is 5 cm more than its height if we reduce the height by 2cm the area of the new rectangle is 60 cm square. How long are the sides of the rectangle?

base = 12 cm

Height = 7 cm

Step-by-step 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