Question

solve for x. each figure is a trapezoid. (plug into midsegment formula)
13)
14)
15)
16)
17)
18)
19)
20)

Explanation:

13)

Step1: Recall mid - segment formula

The mid - segment formula of a trapezoid is $m=\frac{b_1 + b_2}{2}$, where $m$ is the length of the mid - segment, and $b_1,b_2$ are the lengths of the bases. Here, $m = 11$, $b_1=14$, $b_2=x + 1$. So, $11=\frac{14+(x + 1)}{2}$.

Step2: Cross - multiply

Multiply both sides by 2: $11\times2=14+(x + 1)$, which gives $22=14+x + 1$.

Step3: Simplify the right side

Combine like terms: $22=x + 15$.

Step4: Solve for x

Subtract 15 from both sides: $x=22 - 15=7$.

14)

Step1: Apply mid - segment formula

The mid - segment formula is $m=\frac{b_1 + b_2}{2}$, with $m = 14$, $b_1=-26 + 4x$, $b_2 = 10$. So, $14=\frac{-26 + 4x+10}{2}$.

Step2: Cross - multiply

$14\times2=-26 + 4x+10$. So, $28=-16 + 4x$.

Step3: Isolate the term with x

Add 16 to both sides: $28+16=4x$, which gives $44 = 4x$.

Step4: Solve for x

Divide both sides by 4: $x = 11$.

15)

Step1: Use mid - segment formula

The mid - segment formula $m=\frac{b_1 + b_2}{2}$, where $m = 18$, $b_1=16$, $b_2=6x-16$. So, $18=\frac{16+(6x - 16)}{2}$.

Step2: Simplify the right side

The numerator $16+(6x - 16)=6x$. So, $18=\frac{6x}{2}=3x$.

Step3: Solve for x

Divide both sides by 3: $x = 6$.

16)

Answer:

$x = 7$