From the diagram we have
Base = [tex]4x+1[/tex]
Height = [tex]x+1[/tex]
Area = Base × Height
126 = [tex](4x+1)(x+1)[/tex] ⇒ Expand the double bracket
126 = [tex] 4x^{2}+5x+1 [/tex] ⇒ Subtract 126 both sides
0 = [tex] 4x^{2}+5x-125 [/tex] ⇒ Factorise the quadratic expression
0 = [tex](x-5)(4x+25)[/tex] ⇒ Equating each factor to zero
[tex]x-5=0[/tex] [tex]4x+25=0[/tex]
[tex]x=5[/tex] [tex]x=- \frac{25}{4} [/tex]
We need the positive value of [tex]x[/tex] so we use [tex]x=5[/tex]
Height = 5+1 = 6
Base = 4(5)+1 = 21
