Question

Write an inequality for x that would give this rectangle a perimeter of at least 300ft

Answer 1

Answer:

The inequality for $x$ is:

$x\geq 142$

Step-by-step explanation:

Given:

Width of rectangle = 3 ft

Height or length of rectangle = $(x+5)$ ft

Perimeter is at least 300 ft

To write an inequality for $x$.

Solution:

Perimeter of a rectangle is given as:

⇒ $2l+2w$

where $l$ represents length of the rectangle and $w$ represents the width of the rectangle.

Plugging in the given values in the formula, the perimeter can be given as:

⇒ $2(x+5)+2(3)$

Using distribution:

⇒ $2x+10+6$

Simplifying.

⇒ $2x+16$

The perimeter is at lest 300 ft. So, the inequality can be given as:

⇒ $2x+16\geq 300$

Solving for $x$

Subtracting both sides by 16.

⇒ $2x+16-16\geq 300-16$

⇒ $2x\geq284$

Dividing both sides by 2.

⇒ $\frac{2x}{2}\geq \frac{284}{2}$

⇒ $x\geq 142$   (Answer)