how do i find the unknown side????????

[notsure]

A 21m long rectanglar shape has one corner cut from it a 45 degress. The cut length is to be 1/2 of the length of the unknown side measured along both sides. If the final area of the shape is to be 210m^2, what is the length of the unkown side???

All I can come up with is 21X? - area of triangle = 210 ????? Im lost please help

 

[Gene]

The area of a 45° triangle is it's (leg squared)/2

 

[Denis]

A 21m long rectanglar shape has one corner cut from it a 45 degress. The cut length is to be 1/2 of the length of the unknown side measured along both sides. If the final area of the shape is to be 210m^2, what is the length of the unkown side???
All I can come up with is 21X? - area of triangle = 210 ????? Im lost please help

x = shorter side of rectangle; equal sides of cutoff triangle = a
area of triangle = a^2 / 2

21x - a^2 / 2 = 210 [1]

a^2 + a^2 = (x/2)^2
2a^2 = x^2 / 4
a^2 = x^2 / 8 [2]

substitute [2] in [1]:
21x - (x^2 / 8) / 2 = 210
21x - x^2 / 16 = 210
336x - x^2 = 3360
x^2 - 336x + 3360 = 0

Use quadratic equation to solve.
Of the 2 solutions, take the one where x < 21.