As show in the graphic, there is a representation of the situation stated in the problem. So in order to calculate the area we have the next equation as a function of x.

Area:

$A=b*h= (6+2x)(11+2x)\\\\A=28=66+12x+22x+4x^2}\\\\Simplifing\\\\4x^2+34x+38=0\\\\$

Solving the equation to find the roots (values of x):

$x=\frac{-b+- \sqrt{b^2-4ac} }{2a}=\frac{-34+-\sqrt{546} }{8} \\\\solving\\\\x=-7.2\\\\x=-1.3\\$

So mathematically there is no real answer, since x is a width must be positive number. And practically the outer area must be bigger than the inner area, and the inner area is given by 6 times 11, or 66 $cm^2$ .

8 0

3 years ago

The volume of a box is given by the expression

Kamila [148]

Answer:

Area = x^2+4x+3

Step-by-step explanation:

The volume of a box is given by the expression

x^3 + 3x^2 - x-3. The height of the box is given by the expression x-1.

volume of the box = Length * width * height

L is the side length of the box;

Given

V(x) = x^3 + 3x^2 - x-3

Factorize

V(x) = x^2(x+3)-1(x+3)

V(x) = (x^2-1)(x+3)

V(x) = (x+1)(x-1)(x+3)

V = LWH

V = Area * Width

Since the height of the box is x - 1

Area = (x+1)(x+3)

Expand

Area = x^2+3x+x+3

Area = x^2+4x+3

3 0

3 years ago

АBC is a right angled triangle. if B = 90°, AC= 96cm, C=30°. AB = cm​

АBC is a right angled triangle. if B = 90°, AC= 96cm, C=30°. AB = cm