Problems in which Two perpendicular cross roads are taken interior of rectangle/square

Two perpendicular cross roads of equal within run through the middle of a rectangular field of length 80m and breadth 60m. If the area of the cross roads is 675backslash m^(2), find the width of the roads.

Problems in which nos are given in ratio and their sum of squares is also given

prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

Problems in which sum(difference) and product of two no is given

Problems in which product of two consecutive no is given

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 kmph and 36 kmph. If first car blows horn of frequency 300 Hz, then the frequency of horn heard by the driver of second car when line joining the cars make 45° angle with the roads will be (Speed of sound = 330 m/s)

Problems in which sum of two no and sum of their reciprocal is given

Two cars are moving on two perpendicular road towards a crossing with uniform speeds of 72km//hr and 3km//hr . If first car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of second car when line joining the cars make 45^@ angle with the roads, will be