Asoccer field has a perimeter of 316 yards. its area is 5,841 square yards. what are the dimensions of the field?
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59 yards x 99 yards

Step-by-step explanation:

Soccer fields are rectangular.  If the width is W and the length is L:

316 = 2W + 2L

5841 = WL

We have two equations and two variables.  Start by solving for one of the variables in the first equation:

316 = 2W + 2L

158 = W + L

W = 158 − L

Substitute into the second equation

5841 = (158 − L) L

5841 = 158 L − L²

L² − 158 L + 5841 = 0

Factor (or use quadratic formula):

(L − 59) (L − 99) = 0

L = 59 or 99

Find W:

W = 99 or 59

Therefore, the dimensions of the soccer field are 59 yards by 99 yards.