Question

q5 )in figure,pm=6 cm, mr=8 cm and qr=26 cm. (2010)find the length of pq

Answer 1

Pm= 6 mr= 8 so pr = 10
Pr= 10, rq = 26
Applying pythagorean again
Then pr = 24

Answer 2

In the given figure, the length of PQ is 24 cm.

Given,

Refer figure. [It is Q. 25 in the figure].

PM = 6 cm,

MR = 8 cm,

QR = 26 cm.

To find,

The length of PQ.

Solution,

It can be seen that the figure given here shows a right-angled triangle PQR, inside which, there is another right-angled triangle PMR which has its hypotenuse on the base PR of ΔPQR.

The required length of the side PQ can be determined using the Pythagoras theorem, as follows. According to Pythagoras theorem,

$hypotenuse^{2} =base^{2} +height^{2} \hfill ...(1)$

Now, in ΔPMR,

PM = 6 cm,

MR = 8 cm.

So, using (1),

$PR^2=6^{2} +8^{2} \\\implies PR^2=36+64\\\implies PR= \sqrt{100}$

⇒ PR = 10 cm.

Further, QR = 26 cm.

Now, PQ can be determined using the above-determined value of PR, and using (1) in ΔPQR as,

$QR^{2} =PQ^2+PR^2$

Rearranging and substituting the values, we get,

$PQ^2=QR^{2} -PR^2$

$\implies PQ^2=(26)^{2} -(10)^2\\\implies PQ^2=676-100\\\implies PQ^2=576\\\implies PQ=\sqrt{576}$

⇒ PQ = 24 cm.

Therefore, in the given figure, the length of PQ is 24 cm.

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