Question

The base of a rectangle is 6 cm longer than its height the area of a rectangle is 91 cm² what is the perimeter of the rectangle? I need help immediately. Thank you in advance!!

Answer 1

Answer: the perimeter of the rectangle is 38 cm

Explanation:

Let h represent the base of the rectangle.

The base of a rectangle is 6 cm longer than its height. This means that the base of the rectangle is

h + 6

The area of the rectangle is 91 cm²

This means that

h(h + 6) = 91

h² + 6h - 91 = 0

h² + 13h - 7h - 91 = 0

h(h + 13) - 7(h + 13) = 0

h - 7 = 0 or h + 13 = 0

h = 7 or h = - 13

Since the height cannot be negative, it means that h = 7 cm

The base is

h + 6 = 7 + 6

base = 13

Perimeter = 2( base + height)

Perimeter = 2(13 + 6) = 2 × 19

Perimeter = 38 cm