Problem 953

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, 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.

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.