A soccer field is 50 yd wide and 90 yd long. If a person walks across the files along the diagonal instead of waking the length and width of the field, how much shorter is the distance?
Find the distance traveled by waking the length and width of the soccer field. This is equal to the sum of the length and the width of the field.
90+50 = 140
Find the length of the diagonal, and subtract it from 140. Thus will tell you how much shorter the distance is when a person walks across the diagonal.
To find the length of the diagonal, use the
Pythagorean Theorem, a2 + b2 + = c2.
Substitute 50 for a and 90 for b.
502 + 902 + = c2
Simplify 502 + 902 .
2500 + 8100 = c2
10600 = c2
Take the square root of both sides.
Find the approximate value of .
Now find the difference.
140 – 102.956 = 37.044
It is approximate 37.044 yards shorter to walk across the diagonal.