Question 1039482
Let's assume one side as x and the other side as y. We have to find the values of x and y

We have two equations and two unknowns. 
The first equation is x*y *1/2 = 105m^2 = area

The second equation is from Pythagorean theorem

x^2 + y^2 = (Sqrt 421m)^2 = 421m

Now we have both equations
x*y *1/2 = 105m^2
x^2 + y^2  = 421m

We can calculate the value of y from the first equation in terms of x and replace the y of the second equation with what we found for x from the first equation.

x*y *1/2 = 105m^2 therefore x*y = 2(105m^2) and then y = 210m^2/x now we can replace y in the second equation with 210m^2/x

x^2 + (210m^2/x)^2 = (421m)^2

x^2 + (210m^2)^2/x^2 = (421m)^2

Lets multiply both sides of the equation by x^2 to get rid of x^2 in the denomination

x^4 + (210m^2)^2 = (421m)^2 *x^2

x^4 - (421m)^2 *x^2 + (210m^2)^2 = 0

This is similar to a quadratic equation Lets assume x^2 = z Then we can rewrite the equation 

z^2 - (421m)^2 *z + (210m^2)^2 = 0 This is a quadratic equation If we solve this quadratic equation we find z in terms of m. For example z = 9m^2 (please note 9m^2 is a hypothetical example. To get the accurate number we have to solve the quadratic equation

If z = 9m^2 then x^2 = 9m^2 and therefore x = 3m Now that we found x we can use one of the equations to find y.
The easiest is to use x.y/2 = 105m^2 we know x = 3m Therefore 3m.y/2 = 105m^2
and this allows us to calculate y in terms of m. We have to multiply both sides by two and then divide both sides by three. To calculate the exact values of x and y of course we have to solve the quadratic equation:
z^2 - (421m)^2 *z + (210m^2)^2 = 0