Question 54049: Geometry. The length of a rectangular playing field is 5 ft less than twice its width.
If the perimeter of the playing field is 230 ft, find the length and width of the field.
Please help.. Thank you!
Answer by anjulasahay(30)   (Show Source):
You can put this solution on YOUR website! Q.The length of a rectangular playing field is 5 ft less than twice its width.
If the perimeter of the playing field is 230 ft, find the length and width of the field.
ANS:
Let the length of the field = a
Let the width of the field = b
We know that the perimeter of the rectangular field = 2*a+2*b
(since rectangle is made up of 4 sides and two opposite sides are equal,
perimeter is the total length of the sides i.e if we open the rectangle and all
its sides are laid down in straight line connected with each other,total length is defined as primeter)
Here according to the question , a = 2 * b - 5
hence perimeter = 2 * a + 2 * b
= 2 * ( 2 * b - 5 ) + 2 * b
= 4 * b - 2 * 5 + 2 * b
= 6 * b - 10
perimeter given is 230 ft.
hence 6 * b - 10 = 230
6 * b = 230 + 10
b = 240 / 6 = 40 ft
hence a = 2 * b - 5 = ( 2 * 40 ) - 5
= 80 - 5 = 75 ft
answer : two sides are length = 75 ft
and width = 40 ft.
you can check the correctness of answer by calculating the perimeter ,
perimeter = 2 * 75 + 2 * 40 = 230 ft
|
|
|
