Area related to a square or rectangular room/hall

A square carpet with an area 169 m^(2) must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?

A square carpet with an area 169 m^(2) must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangualar room. What is the area of rectangular room?

What would be the length of the diagonal of a square plot whose area is equal to the area of a rectangular plot of 50 m length and 40.5m width?

Find the length of side of a square playground whose area is equal to the area of a rectangular field of dimensions 72m and 338m.