Answer: the perimeter of the rectangle is 38 cm
Step-by-step 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
