Question

280 m350 m395 m553 m• not drawn to scaleIf Chang jogs one lap around the inside track, how far does he jog?A. 675 mB. 845 mC. 1183 mD. 1277 m

Answer 1

Since they are similar triangles, then it is true that

$\frac{a}{p}=\frac{b}{q}=\frac{c}{r}$

So, in this case, you have

$\frac{b}{q}=\frac{553\text{ m}}{395\text{ m}}=1.4$

Then

$\begin{gathered} \frac{c}{r}=1.4=\frac{350\text{ m}}{r} \\ 1.4=\frac{350\text{ m}}{r} \\ r\cdot1.4=\frac{350\text{ m}}{r}\cdot r \\ r\cdot1.4=350\text{ m} \\ \frac{r\cdot1.4}{1.4}=\frac{350\text{ m}}{1.4} \\ r=250\text{ m} \end{gathered}$

On the other hand,

$\begin{gathered} \frac{a}{p}=1.4 \\ \frac{280m}{p}=1.4 \\ \frac{280m}{p}\cdot p=1.4\cdot p \\ 280m=1.4p \\ \frac{280m}{1.4}=\frac{1.4p}{1.4} \\ 200m=p \end{gathered}$

Finally, finding the perimeter of the triangular track, that is, adding the sides

$200m+250+395m=845m$

Therefore, If Chang jogs one lap around the inside track, he runs 845 meters and the correct answer is B. 845 m.