The length of a new rectangular playing field is 4 yards longer than triple the width. If the perimeter of the rectangular playing field is 424 yards, what are its dimensions?
The length of a new rectangular playing field is 4 yards longer than triple the width means:
L = 3 W + 4
P = 2 ( L + W )
424 = 2 ( 3 W + 4 + W )
424 = 2 ( 4 W + 4 )
Divide both sides by 2
212 = 4 W + 4
Subtract 4 to both sides
208 = 4 W
Divide both sides by 4
52 = W
W = 52 yd
L = 3 W + 4
L = 3 ∙ 52 + 4
L = 156 + 4
L = 160 yd
273 yards
88 yard
Ah, the mysterious rectangular playing field. Let's unveil its secrets, shall we?
Let's call the width of this magical field "W". According to the riddle, the length of the field is "4 yards longer than triple the width." So, the length can be magically calculated as 3W + 4.
Now, let's work our funny math magic. The perimeter of a rectangle can be calculated by adding up all its sides. For this field, it is given as 424 yards. So we can make the following equation:
2W + 2(3W + 4) = 424
Now, let my magical calculator do the calculations...
Good news! The width of our rectangular playing field is 46 yards. And the length? It's 3 times the width plus 4, which in this case is 138 + 4. So, the length is 142 yards.
Voila! The dimensions of our magical rectangular playing field are 46 yards wide and 142 yards long. Have a great game!
To find the dimensions of the rectangular playing field, we need to set up an equation based on the given information.
Let's assume the width of the rectangular playing field is 'w' yards.
According to the problem, the length of the playing field is 4 yards longer than triple the width. So, the length can be expressed as (3w + 4) yards.
We know that the formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Therefore, in this case, the equation for the perimeter of the rectangular playing field is:
424 = 2(3w + 4) + 2w
Simplifying the equation, we get:
424 = 6w + 8 + 2w
Combining like terms, we have:
424 = 8w + 8
Next, we isolate the variable by subtracting 8 from both sides of the equation:
416 = 8w
Now, we solve for w by dividing both sides of the equation by 8:
w = 416/8 = 52
Therefore, the width of the rectangular playing field is 52 yards.
To find the length, we substitute the value of w back into the expression for the length:
Length = 3w + 4 = 3(52) + 4 = 156 + 4 = 160
Hence, the dimensions of the rectangular playing field are 52 yards (width) and 160 yards (length).