A fence around a yard (50 yards by 40 yards) is 1.5 yards wide. What is the perimeter and area of the yard, including the fence? By what percent did the area increase?

Respuesta :

The lenght of the yard plus a fence around this yard will be: 50 yd+2(1.5 yd)=53 yd
The width of the yard plus a fence a fence around this yard will be: 40 yd + 2(1.5 yd)=43 yd.

Data:
New lenght (yard +fence)=53 yd
New width (yard+fence)=43 yd

Perimeter of a rectangle=2(lenght) + 2(width)
Perimeter of this yard, including the fence: 2(53 yd)+2(43 yd)=192 yd

Area of a rectangle=lenght x width
Area of this yard, including the fence:(53 yd)(43 yd)=2279 yd².

Now, we calculate the increase area percent:
1)we calculate the old area:
Data:
lenght=50 yd
width=40 yd
Old area=(50 yd)(40 yd)=2000 yd²

2)we calculate: How many yards²  has the area of the yard increased?
Yards gained=2279 yd² - 2000 yd²=279 yd².

3) Now, at last,  What percent did the area increase:

2000 yd²-------------------------------100%
279 yd²----------------------------------  x
x=(279 yd² * 100%) / 2000 yd²=13.95%

Answer:The perimeter of the yard, including the fence would be 192 yd, the area of the yard, including the fence would be 2279 yd², and the percent of the area increase would be: 13.95%.