Area = 1/2 * product of the 2 legs
let 2 legs be x and y m long . Then:-
0.5xy = 35.........................(1)
x^2 + y^2 = (sqrt149)^2
x^2 + y^2 = 149................(2)
From equation (1) :- y = 35 / 0.5x = 70 / x
Substituting in equation (2)
x^2 + (70/x)^2 = 149
x^4 + 4900 = 149x^2
x^4 - 149x^2 + 4900 = 0
(x^2 - 100)(x^2 - 49) = 0
x^2 = 100 or x^2 = 49
x = 10 , y = 7
Lengths of the legs are 7 and 10 m Answer
