Question

How do you solve this: In ?PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.

Answer 1

Answer:

PR = 17 cm

Step-by-step explanation:

Given  :

In ΔPQR,

PQ = 39 cm

PN is an altitude.

QN = 36 cm

RN = 8 cm.

To Find : Length of PR

Solution :

Since we are given that PN is an altitude .

So, PN divides ΔPQR in two right angled triangles named as ΔPQN and ΔPRN. (Refer attached file)

So, first we find Length of PN in ΔPQN using Pythagoras theorem i.e.

$(Hypotenuse)^{2}=(Perpendicular)^{2} +(Base)^{2}$

$(PQ)^{2}=(PN)^{2} +(QN)^{2}$

$(39)^{2}=(PN)^{2} +(36)^{2}$

$1521=(PN)^{2} +1296$

$1521 -1296=(PN)^{2}$

$225=(PN)^{2}$

$\sqrt{225} = PN$

$15 = PN$

Thus, Length of PN = 15cm

Now to find length of PR we will use Pythagoras theorem in ΔPRN.

$(PR)^{2}=(PN)^{2} +(NR)^{2}$

$(PR)^{2}=(15)^{2} +(8)^{2}$

$(PR)^{2}=225 +64$

$(PR)^{2}=289$

$PR= \sqrt{289}$

$PR= 17$

Hence the length of PR = 17 cm