Question

The diagram shows two joined rectangles.
The total area of the compound shape ABCDEF is 36 cm^(2)
By considering the areas of the two rectangles, show that 2x^(2)-5x-18=0 and hence find the value of length AB
Note: Please make sure your final line only shows your final answer written as AB=

Answer 1

Answer:

given that In rectangle DEF..

DE = (x-2) cm

EF = CD+AB

=2x+x

= 3x

Area of DEF.. rectangle = (x-2) (3x)

= 3x²-6x equation 1

In rectangle ABC..

AB=x cm

CB =(x-4) cm

Area of ABC.. = (x) (x-4)

= x²-4x

Total area of compound shape ABCDEF = 36

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0

dividing by 2

2x²-5x-18=0 hence proved.

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0

2x-9 =0,x+2=0

x=9/2 or -2

side never be negative so we take positive value of x=9/2

AB=9/2

mark as briliant

Answer 2

Given:

The compound shape $A$$BC$$DE$$F$ is $36cm^{2}$ by considering the areas two rectangles $2x^{2}-5x-18=0$.

To find:

Find the value of length $AB$.

Step-by-step explanation:

$2x^{2}-5x-18=0$

$2x^{2}-5x-36=0$

$2x^{2}+4x-9x-36=0$

$2x(x+2)-9(x+2)=0$

$(2x-9)(x+2)=0$

$2x-9=0$

$2x=9$

$x=\frac{9}{2}$

$x+2=0$

$x=-2$

Answer:

Therefore, The value of length $AB$ value $\frac{9}{2},-2$.