what is the length of $overline{aj}$ if $overline{ab}paralleloverline{jk}$?\n8 in.\n8.75 in.\n10.25 in.\n14…

Explanation:

Step1: Use similar - triangle property

Since $\overline{AB}\parallel\overline{JK}$, $\triangle HAB\sim\triangle HJK$. Then, the ratios of corresponding sides are equal. That is, $\frac{HA}{HJ}=\frac{HB}{HK}$. Let $AJ = x$, then $HJ=HA + AJ=5.25 + x$. And $HK=HB + BK=3 + 5 = 8$ inches, $HA = 5.25$ inches, $HB = 3$ inches. So, $\frac{5.25}{5.25 + x}=\frac{3}{8}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{5.25}{5.25 + x}=\frac{3}{8}$ gives us $5.25\times8=3\times(5.25 + x)$. $42 = 15.75+3x$.

Step3: Solve for $x$

Subtract $15.75$ from both sides: $42−15.75 = 3x$. $26.25 = 3x$. Divide both sides by $3$: $x=\frac{26.25}{3}=8.75$ inches.

Answer:

8.75 in.