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?

**Solution:-**

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, a^{2} + b^{2} + = c^{2}.

Substitute 50 for a and 90 for b.

50^{2} + 90^{2} + = c^{2}

Simplify 50^{2} + 90^{2} .

2500 + 8100 = c^{2}

10600 = c^{2}

Take the square root of both sides.

c =

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.