Answer:
The dimension are 10 inches by 8 inches
Step-by-step explanation:
The rectangular cutting has a perimeter of 36 inches . The area is 80 inches². The dimension can be solved as follows :
perimeter of a rectangle = 2l + 2b
where
l = length
b = breadth
36 = 2l + 2b..............(i)
Area of a rectangle = l × b = lb
80 = lb........................(ii)
l = 80/b
Insert the value of l in equation (i)
36 = 2(80/b) + 2b
36 = 160/b + 2b
36 = (160 + 2b²)/b
cross multiply
36b = 160 + 2b²
2b² - 36b + 160 = 0
b² - 18b + 80 = 0
(b - 8)(b - 10)
b = 8 or b = 10
let us insert b in equation (ii)
80 = lb........................(ii)
80 = l8
l = 80/8
l = 10
or if we insert b =10
80 = lb........................(ii)
80 = 10l
l = 8
The dimension are 10 inches by 8 inches
