Answer: PQ = 18 unit.
Explanation: Since, according to question,
.
Therefore, by the property of similar triangles the ratio of corresponding sides must be equal.
Here, The right angle are at A in
and at Q in
respectively.
Moreover,
is congruent to
and
is congruent to
.
Therefore, AB, BC and AC are corresponding to sides PQ, QR and PR respectively.
Thus, we can write, ![\frac{AB}{PQ} =\frac{BC}{QR} =\frac{AC}{PR}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BPQ%7D%20%3D%5Cfrac%7BBC%7D%7BQR%7D%20%3D%5Cfrac%7BAC%7D%7BPR%7D)
⇒![\frac{AB}{PQ} =\frac{BC}{QR}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BPQ%7D%20%3D%5Cfrac%7BBC%7D%7BQR%7D)
⇒
( because, here, AB= 6, BC=8 and QR=24)⇒ PQ=18