The area of a right triangle is 35m^2. The hypotenuse has a length of the square root of 149 m. What are the lengths of the legs? (one answer) ?

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