Let one side (AB) = (x – 4)m
Other side (BC) = x m
and hypotenuse = 20 m
We know,
AC2 = AB2 + BC2
⇒ (20)2 = (x – 4)2 + (x)2
⇒ 400 = x2 + 16 – 8x + x2
⇒ 400 = 2x2 – 8x + 16
⇒ 2x2 – 8x – 384 = 0
⇒ 2(x2 – 4x –192) = 0
⇒ x2– 4x – 192= 0
Therefore, the required representation in the form of quadratic equation be x2– 4x –192 = 0.