Answer:
Length = 12 ft
Width = [tex] \frac{7}{2} ft[/tex]
Step-by-step explanation:
Given,
Area of rectangle = [tex]42 \: {ft}^{2} [/tex]
Width = X
Length = 2x + 5
Now,
[tex]x(2x + 5) = 42[/tex]
[tex]2 {x}^{2} + 5x = 42[/tex]
[tex]2 {x}^{2} + 5x - 42 = 0[/tex]
[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]
[tex]2x(x + 6) - 7(x + 6) = 0[/tex]
[tex](2x - 7)(x + 6) = 0[/tex]
Either
[tex]2x - 7 = 0[/tex]
[tex]2x = 0 + 7[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} [/tex]
Or,
[tex]x + 6 = 0[/tex]
[tex]x = 0 - 6[/tex]
[tex]x = - 6[/tex]
Negative value can't be taken.
So, width = [tex] \frac{7}{2} ft[/tex]
Again,
Finding the value of length,
Length = [tex]2x + 5[/tex]
[tex]2 \times \frac{7}{2} + 5[/tex]
[tex]7 + 5[/tex]
[tex]12[/tex]
Length = 12 ft
