Question

(13) the perimeter of the rectangle is 26cm. find the length.
rectangle with length x and width 6
x = ______
(14) solve for x.
angle diagram with (2x + 20)° and (2x)° forming a linear pair
x = ______
(15) solve for x.
\\(\frac{x}{6} = 15\\)
x = ______
(16) three or more points that lie on the same line are called ______.
a) perpendicular
b) corresponding
c) collinear
d) obtuse
(17) which value of x will make the lines perpendicular?
angle diagram with (x - 10)° and options a) 90, b) 95, c) 100, d) 105
(18) the figure below is called a ______.
diagram of ray rs
a) line
b) line segment
c) point
d) ray

Explanation:

Question 13:

Step1: Recall rectangle perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is length and \( w \) is width. Here, \( w = 6 \), \( l = x \), and \( P = 26 \). So, \( 26 = 2(x + 6) \).

Step2: Solve for \( x \)

Divide both sides by 2: \( \frac{26}{2} = x + 6 \) → \( 13 = x + 6 \). Subtract 6 from both sides: \( x = 13 - 6 = 7 \).

Step1: Recognize supplementary angles

The two angles form a linear pair, so they are supplementary (sum to \( 180^\circ \)). Thus, \( (2x + 20) + 2x = 180 \).

Step2: Solve the equation

Combine like terms: \( 4x + 20 = 180 \). Subtract 20: \( 4x = 160 \). Divide by 4: \( x = \frac{160}{4} = 40 \).

Step1: Solve the proportion

Given \( \frac{x}{6} = 15 \), multiply both sides by 6: \( x = 15 \times 6 \).

Step2: Calculate the product

\( 15 \times 6 = 90 \), so \( x = 90 \).

Answer:

7

Question 14: