%) 1.3.27 Question Help
The length of a new rectangular playing field is 6 yards longer than double the width. If the perimeter of the rectangular playing field
is 312 yards, what are its dimensions?
The width is yards

Width of field  = 50 yards

Length of Yards =  106 yards

Step-by-step explanation:

Let the width of field be x yards

given that "The length of a new rectangular playing field is 6 yards longer than double the width"

Length of Yards= 2*width of field + 6 = 2x+6 yards

perimeter of the rectangular playing field  = 312 yards

We know that perimeter of rectangle is given by 2(length + width ).

Since field is rectangular then

2(length + width ) = 312

2(x+2x+6) = 312

=> 3x+6 = 312/2 = 156

=> 3x = 156 - 6 = 150

=> x = 150/3 = 50

Thus,

Width of field is x = 50 yards

Length of Yards=  2x+6 yards = 2*50+6  yards = 106 yards

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.