What are the dimensions of a soccer field if the perimeter is 300 years and the length is 50 yards longer than the width?

Question

Eva Adamson · Accepted Answer

width = 50 and length = 100 For simplicity, we will use the letters W for width, L for length and P for perimeter. For a rectangular field
#P = 2 * (L + W)#
So we have
#2 * (L + W) = 300#
or #L + W = 150# We are told that
#L = W + 50#
So #L + W = 150# can be re-written as #(W+50) + W = 150#
which can be simplified:
#2W + 50 = 150#
#2W = 100#
#W = 50# And since #L = W +50#
#L = 50 + 50 = 100# Therefore the width is 50 (yards) and the length is 100 (yards).

Hazel Anglin · Answer

undefined Let's denote the width of the soccer field as $ w $ yards. Since the length is 50 yards longer than the width, the length can be represented as $ w + 50 $ yards.

Given that the perimeter is 300 yards, we can write the equation:

$$ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) $$

Substituting the expressions for length and width into the equation:

$$ 300 = 2 \times ((w + 50) + w) $$

Solving for $ w $:

$$ 300 = 2 \times (2w + 50) $$

$$ 300 = 4w + 100 $$

$$ 4w = 200 $$

$$ w = 50 $$

So, the width of the soccer field is 50 yards, and the length is $ 50 + 50 = 100 $ yards. Therefore, the dimensions of the soccer field are 100 yards by 50 yards.