Question

the diagonal of a rectangle field 60 m more than the shorter side .if the longer side is 30 m more than the shorter side .find the sides of thf field ? plz solve this by quadratic formula

Answer 1

Answer:

Shorter Side = 90 m

Longer Side = 120 m

Diagonal  = 150 m

Step-by-step explanation:

Let say Shorter side of Rectangle = L m

The  longer Side of Rectangle = L + 30 m

Diagonal of Field = Shorter Side + 60 m

=> Diagonal of Field = L + 60 m

Diagonal ² = Shorter Side² + Longer Side²

=> ( L + 60)² = L² + (L + 30)²

=> L² + 3600 + 120L = L² + L² + 900 + 60L

=> 0 = L² - 60L - 2700

=> L² - 60L - 2700 = 0

=> L² - 90L + 30L - 2700 = 0

=> L (L - 90) + 30 (L - 90) = 0

=> L = 90   as L can not be negative

Shorter Side = 90 m

Longer Side = 90 + 30 = 120 m

Diagonal  = 90 + 60 = 150 m