Question

30. A man walks diagonally from one corner of a
rectangular lot to the opposite corner. If he
walks at the rate of 5 feet a second, and the lot is
50 feet by 120 feet, how many seconds will he
save by walking diagonally instead of walking
along the perimeter of the lot?
(A)8
(B) 10
(C) 17
(D) 34

1. The time he saves when walking diagonally is 8 seconds

### How to find diagonal and side of a rectangle?

A rectangle has opposite sides equal to each other.
The angles are equal.
Therefore,
perimeter of a rectangle = 2l + 2w
where
• l = length
• w = width
Therefore,
distance of the diagonal  =√ 50² + 120²
distance of the diagonal  = √2500 + 14400
distance of the diagonal = √16900
distance of the diagonal = 130 feet
distance if he follows the length of the rectangle = 50 + 120 = 170 feet
Hence,
Time spent diagonally
5 = 130 / t
t = 130 / 5
t = 26 seconds
Time spent along the perimeter
5 = 170 / t
t = 170 / 5
t = 34 secods
Therefore,
Time he will save by walking diagonally = 34 – 26 = 8 seconds