Respuesta :
Answer:
[tex] P= 456 = 2X +2Y[/tex] (1)
And for this case we know the following condition "The length of the field is 7 yards less than quadruple the width" and we can write this :
[tex] X = 4Y -7[/tex]
And replacing into equation (1) we got:
[tex] 456= 2(4Y-7) +2Y[/tex]
[tex] 456 = 8Y -14 +2Y[/tex]
[tex] 456 = 10Y-14[/tex]
Adding 14 in both sides we got:
[tex] 456+14 = 10Y[/tex]
And dividing 10 on both sides we got:
[tex] Y=\frac{470}{10}= 47[/tex]
And then we can solve for X and we got:
[tex] X= 4*47 -7=181[/tex]
Step-by-step explanation:
For this case we can set up the following notation:
X represent the lenght
Y represent the width
And since we have a rectangular playing filed the perimeter is given by:
[tex] P= 456 = 2X +2Y[/tex] (1)
And for this case we know the following condition "The length of the field is 7 yards less than quadruple the width" and we can write this :
[tex] X = 4Y -7[/tex]
And replacing into equation (1) we got:
[tex] 456= 2(4Y-7) +2Y[/tex]
[tex] 456 = 8Y -14 +2Y[/tex]
[tex] 456 = 10Y-14[/tex]
Adding 14 in both sides we got:
[tex] 456+14 = 10Y[/tex]
And dividing 10 on both sides we got:
[tex] Y=\frac{470}{10}= 47[/tex]
And then we can solve for X and we got:
[tex] X= 4*47 -7=181[/tex]
