Rectangle to squares

[miamivince]

A rectangle of lngth 100 cms and width 50 + x is divided into a square and a remainder. This is done 6 times until six new squares are formed. the remainder forms the basis for each new square. Their combined area is the same as the rectangle. Find the value for x ? If their was a geometric relationship between the new squares , we could use a geometric progresion formula . x is betwen 10 and 45 is the only other info given. Thanks. Could applied differentiation be used ?

 

[HallsofIvy]

Even without a geometric series it would be straightforward, if tedious, to just do the calculations six times. Doing the subdivisions a few times might let you see a pattern. Have you tried finding the squares? One thing you may want to consider is whether x is less than or larger than 50.