In △PQR, the measure of angle Q is 90
∘
. If tanP=
3
4
​
and PQ=1.5cm, then what is the length (in cm) of side PR?

In right-angled △PQR at Q:
tanP=
Adjacent side
Opposite side
​
=
PQ
QR
​

Given that tanP=
3
4
​
:

PQ
QR
​
=
3
4
​

We are given PQ=1.5cm. Substituting this into the ratio:

1.5
QR
​
=
3
4
​

QR=
3
4
​
×1.5=4×0.5=2cm
Now, using Pythagoras theorem in △PQR:

PR
2
=PQ
2
+QR
2

PR
2
=(1.5)
2
+(2)
2

PR
2
=2.25+4=6.25
PR=
6.25

​
=2.5cm
Thus, the length of side PR is 2.5cm.