Question

part b
c. find the width if the perimeter is 58 millimeters. explain how you can check that your answer is correct.
solving 58 = 8x +
for x, the width is found to be
mm. to check that this answer is correct, use the value of the width to
determine the length.
the sum of all four sides, 23+
+6 + 6, should equal
d. on a separate sheet of paper, use a ruler to draw and label $overline{pq}$, which is congruent to the segment representing the length of rectangle wxyz. what is the measure of $overline{pq}$?

mm

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2l+2w$, where $P$ is perimeter, $l$ is length and $w$ is width. Given $P = 58$ mm. Assume length $l = 23$ mm and width $w=x$. So $P=2l + 2w$ becomes $58=2\times23+2x=46 + 2x$. Rearranging gives $58=2x + 46$, and we can rewrite it as $58=8x+10$ (assuming some previous - step relationship). Solving $58=8x + 10$ for $x$:
First, subtract 10 from both sides: $58-10=8x$, so $48 = 8x$. Then divide both sides by 8: $x = 6$ mm.

Step2: Check the answer

To check, we use the values of length and width in the perimeter formula. The length is 23 mm and width is 6 mm. The sum of the four - sides of the rectangle is $23+23 + 6+6$.
The sum of all four sides, $23+23+6 + 6=58$ mm.

Answer:

The blanks should be filled as follows:
In the equation $58 = 8x+10$, the second blank (width) is 6 mm.
The third blank (to complete the sum of sides for checking) is 23.
The fourth blank (the perimeter value for checking) is 58.
For part d, since the length of rectangle $WXYZ$ is 23 mm, the measure of $\overline{PQ}$ is 23 mm.