Question

2 a rectangle has the following dimensions.
a) the rectangle has a width of 8.5x inches.
b) the rectangle has a length of 16 inches.
the perimeter is 100 inches.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(\text{length} + \text{width})$.
Substitute the given values: $100 = 2(16 + 8.5x)$

Step2: Simplify the equation

Divide both sides by 2:
$\frac{100}{2} = 16 + 8.5x$
$50 = 16 + 8.5x$

Step3: Isolate the variable term

Subtract 16 from both sides:
$50 - 16 = 8.5x$
$34 = 8.5x$

Step4: Solve for $x$

Divide both sides by 8.5:
$x = \frac{34}{8.5}$
$x = 4$

Step5: Calculate the width

Substitute $x=4$ into the width expression:
$\text{Width} = 8.5x = 8.5 \times 4$

Answer:

a) $x = 4$
b) The width of the rectangle is 34 inches.