Answer to Question #229170 in Algebra for Maj

Question

Assessment

Solve the following.

1. The perimeter of a rectangle is 24 cm. Express the area of the rectangle in terms of the width x.

2. The area of a rectangle is 85 cm. Express the perimeter of the rectangle as a function of the width x.

3. A piece of wire y cm long is bent into a circle. Express the area of the circle as a function of the circumference y.

4.  Express the length of the radius of a circle as a function of the 

5. Express the length of the diameter of a circle as a function of the circumference.

6.The perimeter of a rectangle is 50 centimeters. Express its area A as a function of the length x.

7. A wire of length x is bent into the shape of a square. Express the area of the square as a function of x. 

Answer 1

1.$Width$ $=$ $x$

$Perimeter=2(L+W)$

$Length=12-x$

Area of a rectangle is represented as: $L\times W$

$Area=x(12-x)$

$Area=12x-x^2$

2.$Width=x$

$Area=L\times W$

$Length=\frac{85}{x}$

$Perimeter=2(\frac{85}{x}+x)$

$Perimeter=\frac{170}{x}+2x$

3.$Circumference=2\pi r$

$y=2\pi r$

$r=\frac{y}{2\pi}$

$Area=\pi r^2$

$Area=\pi \times(\frac{y}{2\pi})^2$

$Area=\pi \times(\frac{y^2}{4\pi^2})$

$Area=\frac{y^2}{4\pi}$

4.$Circumference=2\pi r$

$y=2\pi r$

$r=\frac{y}{2\pi}$

5. $r=\frac{y}{2\pi}$

$diameter=r+r=2r$

$2r=2(\frac{y}{2\pi})$

$2r=\frac{y}{\pi}$

6.$Length=x$

$Width=25-x$

$A=L\times W$

$A=x(25-x)$

$A=25x-x^2$

7.$Perimeter$ $of$ $a$ $square=x$

Since all sides of a square are equal:

$Length$ $of$ $a$ $sqaure=\frac{x}{4}$

$Area=Side\times Side=S\times S$

$Area=\frac{x}{4} \times \frac{x}{4}$

$Area=\frac{x^2}{16}$