Step 1: Problem
Area of a rectangle.
Step 2: Concept
Area of a rectangle = Length x width
Draw the diagram with a label.
Step 3: Method
Area of original rectangle = Length x width
= x(x + 6)
[tex]=x^2\text{ + 6x}[/tex]Find the area of the new ractangle.
Area = Length x width
= (x + 10)(x + 4)
[tex]\begin{gathered} x^2\text{ + 4x + 10x + 40} \\ x^2\text{ + 14x + 40 } \\ x^2\text{ + 14x + 40 } \\ x^2\text{ + 14x }+\text{ 40} \end{gathered}[/tex]New area - Original area = 104
[tex]\begin{gathered} x^2+14x+40-(x^2\text{ + 6x) = 104} \\ x^2+14x+40-x^2\text{ - 6x = 104} \\ 8x\text{ + 40 = 104} \\ 8x\text{ = 104 - 40} \\ 8x\text{ = 64} \\ x\text{ = }\frac{64}{8} \\ \text{x = 8} \end{gathered}[/tex]Step 4: Final answer
Area of the original figure = x(x + 6)
= 8(8 + 6)
= 8 x 14
= 112 in square
