Question

A youth soccer field has a perimeter of 320 yards and its length measures 40 yards more than its width.

Answer 1

(1) The measure of the width of the given youth soccer field is 60 yards.

(2) The measure of the length of the given youth soccer field is 100 yards.

(3) The distance diagonally across the youth soccer field is 116.62 yards.

The given parameters;

• perimeter of the field, P = 320 yards

• length of the field, L = 40 + W

(1) The width of the soccer field is calculated as;

P = 2(L + W)

320 = 2(40 + W + W)

320 = 2(40 + 2W)

320 = 80 + 4W

4W = 320 - 80

4W = 240

$W = \frac{240}{4} \\\\W = 60 \ yards$

(2) The length of the soccer field is calculated as;

L = 40 + W

L = 40 + 60

L = 100 yards

(3) The the distance diagonally across the youth soccer field;

$d^2 = L^2 + W^2\\\\d^2 = 100^2 + 60^2\\\\d^2 = 13600\\\\d = \sqrt{13600} \\\\d = 116.62 \ yards$

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