Please help!
The painting shown at the right has an area of 240 . What is the value of x?

X =? In.

Take x = 10.2 in. or x = 10 in.

Step-by-step explanation:

Given :

Length = (2x+3) in.

Breadth = x in.

Also, the Area of Rectangle = 240 sq in.

We know that,

Area of Rectangle = length x breadth

240 = (2x+3) x

2x² + 3x = 240

2x² + 3x - 240 = 0

Solving    2x²+3x-240 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B²-4AC

x =   ————————

                     2A

In our case,  A   =     2

                     B   =    3

                     C   =  -240

Accordingly, B²  -  4AC   = 9 - (-1920) = 1929

Applying the quadratic formula :

              -3 ± √ 1929

  x  =    ——————

                     4

 √ 1929   , rounded to 4 decimal digits, is  43.9204

So now we are looking at:

          x  =  ( -3 ±  43.920 ) / 4

Two real solutions:

x =(-3+√1929)/4=10.230 ≈ 10

or

x =(-3-√1929)/4=-11.730

We'll take x = +ve value for calculation of length and breadth.

Therefore,

Length = [2(10.2) + 3 ]

L = 23.4 in.

Breadth = 10.2 in.

OR

Length = [2(10) + 3]

L = 23 in.

Breadth = 10 in.

step-by-step explanation: