Answer:
[tex]x=5[/tex]
Dimensions of rectangle are
W=14 and L = 3
Step-by-step explanation:
Are of rectangle is
[tex]A=WL[/tex] --------(1)
Where W is width and L is length of rectangle
Here
A=60
W=x+9
L=x-2
Substituting values in equation (1)
[tex]60 = (x+9) (x-2)[/tex]
[tex]60 = x^{2} +9x -2x -18[/tex]
[tex]x^{2} + 7x - 78 = 0[/tex]
Using quadratic formula
[tex]x=\frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
Here a=1, b=7 and C=-78
[tex]x= \frac{-7 +/- \sqrt{7^{2} - 4(-78)} }{2}[/tex] (Here +/- = ±)
[tex]x= \frac{-7 +/- \sqrt{ 49 + 312} }{2}[/tex]
[tex]x= \frac{-7 +/- \sqrt{ 361} }{2}\\x= \frac{-7+/- 19}{2}[/tex][tex]x= \frac{-7 + 19 }{2} \ \ and \ \ x= \frac{-7-19 }{2}[/tex]
[tex]x= \frac{12 }{2} \ \ and \ \ x= \frac{-26 }{2}[/tex]
[tex]x= 5 \ \ and \ \ x= -13[/tex]
x cannot be negative (Negative x means -ve dimensions of rectangle). Therefore
[tex]x=5[/tex]
Dimensions of the rectangle are
[tex]W=x+9 = 5+9 = 14[/tex]
[tex]L= x - 2 = 5-2 = 3[/tex]
