Similar Triangles: PQ, XY (=7.5cm), SR parallel; QY=13.5cm, YR=9cm

[richiesmasher]

Hello, I have a question here which is giving me some problems. The question is in the picture below.



I have already figured out number (i) Which is that all corresponding angles are equal, so therefore the triangles are similar (A.A.A) rule.

But I simply cannot figure out (ii) or (iii).

I know that in similar triangles the the ratio between the sides is the key, and if I seperate those triangles I can clearly see which sides correspond, but I cant figure out the length still.

Can anyone help with step by step explanations?

 

[barrick]

Hi richiesmasher,

I understand that 7.5cm is the length of XY.

For part (ii), note that the triangles XQY and SQR are similar, and the same holds for XRY and PRQ.

For part (iii), use the fact that the ratio of the areas of similar figures is the square of the ratios of the corresponding lengths.

 

[richiesmasher]

Similar Triangles

Hi richiesmasher,

I understand that 7.5cm is the length of XY.

For part (ii), note that the triangles XQY and SQR are similar, and the same holds for XRY and PRQ.

For part (iii), use the fact that the ratio of the areas of similar figures is the square of the ratios of the corresponding lengths.

Hi, thank you for the info for part (ii), I worked it out to be 12.5 for RS and 18.75 for PQ .

But I'm still having some trouble understanding part (iii) I understand now that the ratio of the corresponding lengths of triangle RXS to triangle PQX is 1.5 since 18.75/12.5 is equal to 1.5, but when I square that it's 2.25, is that really correct?