Let's name the a, b, c
let side a = x
let side b = 4+x
Let side c = hypotenuse = 20
Using the law of pythagoras
opposite² + adjacent² = hypotenus²
x² + (x+4)² = 20²
open the parenthesis
x² + x² + 4x +16 = 400
2x² + 4x + 16 = 400
2x² + 4x + 16 - 400 = 0
2x² + 4x - 384 = 0 --------------------------------(1)
The is now a quadratic equation
so we will solve and find x
Using the formula method
Quadratic formula is
[tex]x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Comparing equation (1) with ax² + bx + c = 0
a = 2 b = 4 and c= -384
Inserting the values into the formula
[tex]x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}[/tex]simplifying the above
[tex]x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}[/tex][tex]undefined[/tex]