Exercise 37 Page 579

Let's analyze the given figure. Since we are given a triangle with two lines that are parallel to one of its sides, we can use the Triangle Proportionality Theorem.

At first we will apply it to △ QSW and RX. The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. QR/RS=QX/XW ⇕ 2/RS=QX/12Since we are given the lengths of XW and QW, we can find the length of QX.

Now we can substitute the missing length into our proportion. 2/RS=QX/12 ⇕ 2/RS=3/12 We will solve it for RS.

Similarly, we can apply the Triangle Proportionality Theorem to △ QTV and SW. Let's write a proportion using the expressions for the lengths of the segments. QS/ST=QW/WV ⇕ QS/5=15/WV Since we know the lengths of QR and RS, we can find the length of QS.

Now we can substitute the missing length into our proportion. QS/5=15/WV ⇕ 10/5=15/WV Let's solve it for WV.

Finally, we found that RS=8 and WV=7.5.