Solve =pirl+pir^2=pir(l+r)

$$= \pi r l + \pi r ^ { 2 } = \pi r ( l + r )$$

Solve for l (complex solution)

$$l\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply \pi r by l+r.

$$\pi rl+\pi r^{2}=\pi rl+\pi r^{2}$$

Subtract \pi rl from both sides.

$$\pi rl+\pi r^{2}-\pi rl=\pi r^{2}$$

Combine \pi rl and -\pi rl to get 0.

$$\pi r^{2}=\pi r^{2}$$

Cancel out \pi on both sides.

$$r^{2}=r^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any l.

$$l\in \mathrm{C}$$

Solve for r (complex solution)

$$r\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply \pi r by l+r.

$$\pi rl+\pi r^{2}=\pi rl+\pi r^{2}$$

Subtract \pi rl from both sides.

$$\pi rl+\pi r^{2}-\pi rl=\pi r^{2}$$

Combine \pi rl and -\pi rl to get 0.

$$\pi r^{2}=\pi r^{2}$$

Subtract \pi r^{2} from both sides.

$$\pi r^{2}-\pi r^{2}=0$$

Combine \pi r^{2} and -\pi r^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any r.

$$r\in \mathrm{C}$$

Solve for l

$$l\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply \pi r by l+r.

$$\pi rl+\pi r^{2}=\pi rl+\pi r^{2}$$

Subtract \pi rl from both sides.

$$\pi rl+\pi r^{2}-\pi rl=\pi r^{2}$$

Combine \pi rl and -\pi rl to get 0.

$$\pi r^{2}=\pi r^{2}$$

Cancel out \pi on both sides.

$$r^{2}=r^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any l.

$$l\in \mathrm{R}$$

Solve for r

$$r\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply \pi r by l+r.

$$\pi rl+\pi r^{2}=\pi rl+\pi r^{2}$$

Subtract \pi rl from both sides.

$$\pi rl+\pi r^{2}-\pi rl=\pi r^{2}$$

Combine \pi rl and -\pi rl to get 0.

$$\pi r^{2}=\pi r^{2}$$

Subtract \pi r^{2} from both sides.

$$\pi r^{2}-\pi r^{2}=0$$

Combine \pi r^{2} and -\pi r^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any r.

$$r\in \mathrm{R}$$