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

`(a)/(p)=(b)/(q)=(c)/(r)`

So, in this case, you have

`(b)/(q)=\frac{553\text{ m}}{395\text{ m}}=1.4`

Then

`\begin{gathered} (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} \\ (r\cdot1.4)/(1.4)=\frac{350\text{ m}}{1.4} \\ r=250\text{ m} \end{gathered}`

On the other hand,

`\begin{gathered} (a)/(p)=1.4 \\ (280m)/(p)=1.4 \\ (280m)/(p)\cdot p=1.4\cdot p \\ 280m=1.4p \\ (280m)/(1.4)=(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.