Problema Solution
The 1999 women’s World Cup Soccer Tournament was played at the Rose Bowl in Pasadena, California. The perimeter of the rectangular filed is 376 yards, and the area of the field is 8352 square yards. Find the dimension of the field.
Answer provided by our tutors
The perimeter of a rectangle is given by
2(length+width)
and area is given by
Length X Width
In the given problem,
Perimeter = 376 yards
And Area = 8352 sq. yards
Therefore,
2(l+w) = 376_________(1)
and l x w = 8352_____(2)
From eq. 2
l = 8352/w
Substituting the value in Eq. (1) we get
2(8352/w + w) = 376
8352+w^2 = 188w
w^2 - 188w + 8352 = 0
w^2-116w-72w+8352=0
w(w-116)-72(w-116)=0
(w-72)(w-116) = 0
Therefore,
w = 72 or 116
So, for
w = 72, l = 188-72 = 116
and for w = 116, l = 72
Therefore,
Length = 116 yards, Width = 72 yards
or
Width = 116 yards, Length = 72 yards