Answer:
a)[tex](x^{2} +14x+40)ft^{2}[/tex]
b)14ft, 8ft
Step-by-step explanation:
a) Area of Rectangle = Length x Breadth
= [tex](x+10)(x+4)\\=x^{2} +4x+10x+40\\=(x^{2} +14x+40) ft^{2}[/tex]
b) Given Area of rectangle = [tex]112ft^{2}[/tex]
[tex]x^{2} +14x+40=112\\x^{2} +14x-72=0 (Quadratic Equation)\\\\[/tex]
Quadratic Equations: [tex]ax^{2} +bx+c = 0\\[/tex]
In this case, a = 1, b = 14, c = -72
[tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a} \\= \frac{-14+/-\sqrt{14^{2} 4(1)(-72)} }{2(1)} \\= 4 or - 18 (reject)[/tex]
We reject negative values.
so x = 4,
The length of table = (x+10) ft = 4+10 = 14ft
The breadth of the table = (x+4) ft = 4 + 4 = 8ft
