Point Q is taken on the segment RS, while the length of the segment RQ is 0.23 of the segment RS

Point Q is taken on the segment RS, while the length of the segment RQ is 0.23 of the segment RS. Find the length of the segment RS if the length of the segment QS is greater than the length of the segment RQ by 16.2 cm.

Let’s write down the known data in mathematical form.

a) RQ = 0.23 RS;

b) QS = 16.2 cm + RQ;

c) RS = RQ + QS.

Substitute into expression c) the data from expression b) (replace QS).

RS = RQ + 16.2 + RQ;

RS = 2 RQ + 16.2.

Substitute the data from expression a) into the resulting expression (replace with RQ).

RS = 2 * 0.23 RS + 16.2;

RS = 0.46 RS + 16.2;

RS – 0.46 RS = 16.2;

0.54 RS = 16.2;

RS = 16.2 / 0.54 (RS = 1620/54 = 30);

RS = 30.

Answer: RS = 30 cm.