What are the dimensions of a rectangular parcel of land?

xy = 1200

d = sqrt (x^2 + y^2)

sqrt (x^2 + y^2) = x + 10

x^2 + y^2 = x^2 + 20x + 100

y^2 = 20x + 100

y^2 = 20(1200/y) + 100

y^3 - 24000 - 100y = 0

y^3 - 100y - 24000 = 0

(y - 30)(y^2 + 30y + 800) = 0

Real solution:

y = 30

x = 40

The length of the rectangular parcel of land

is 40 meters and its width is 30 meters.

Length = L m

Breadth = B m

Area = LB=1200 m² →B=1200/L

Also Diagonal =√(L²+B²) =L+10 10 m longer than one side of the parcel.

Squaring both sides gives

→L²+B² =L²+100+20L

i.e B²=100+20L

Since LB=1200 →L²B²=1440000

Hence L²(100+20L)=1440000

100L²+20L³=1440000

i.e 5L²+L³=72000

By hit and trial L=40 m

Hence B=1200/L=1200/40= 30 m