Question

the diagonal of a rectangular field is 60 metre more than its breadth if its length is 30 more than the breadth find the length and breadth of the field​

Answer 1

Let length of shorter side = x m

Length of bigger side = (x + 30) m

Length of diagonal = (x + 60) m

We have to use Pythagoras theorem,

$(Diagonal) ^2 = (Bigger side)^2 + (Shorter side)^2$

(x + 60)² = (x + 30)² + x²

x² + 120x + 3600 = x² + 60x + 900 + x²

60x + 2700x = x²

x² - 60x - 2700 = 0

x² - 90x + 30x - 2700 = 0

x(x - 90) + 30(x - 90) = 0

x = -30 and 90 but x ≠ -30

Hence, Length of shorter side = 90 m

Length of bigger side = 120 m