Question

The area of a parallelogram is given by the formula A=bh the area of the parallelogram on the right is 126 sq units. Find its base and height

Answer 1

From the diagram we have

Base = $4x+1$
Height = $x+1$

Area = Base × Height
126 = $(4x+1)(x+1)$ ⇒ Expand the double bracket
126 = $4x^{2}+5x+1$ ⇒ Subtract 126 both sides
0 = $4x^{2}+5x-125$ ⇒ Factorise the quadratic expression
0 = $(x-5)(4x+25)$ ⇒ Equating each factor to zero

$x-5=0$                       $4x+25=0$
$x=5$                           $x=- \frac{25}{4}$

We need the positive value of $x$ so we use $x=5$

Height = 5+1 = 6
Base = 4(5)+1 = 21