Question

In triangle PQR, seg PM is a median, PM = 9 and PQ2 + PR2 = 290. Find the length of QR​

Answer 1

Answer:

Explanation:

Given :

• In ΔPQR , seg PM is a median.
• PM = 9 , PQ² + PR² = 290

To Find :

• The length of QR.

Solution :

Given that, In ΔPQR, seg PM is a median.

By appollonius theorem ::

PQ² + PR² = 2PM² + 2QM²

=> 290 = 2 × 9² + 2QM²

=> 290 = 162 + 2QM²

=> 290 - 162 = 2QM²

=> 128 = 2QM²

=> 128/2 = QM²

=> 64 = QM²

=> QM = 8 units

Now,

QR = 2 × QM

=> QR = 2 × 8

=> QR = 16 units

Hence :

The length of side QR is 16 units.

Answer 2

Given -

• In ∆PQR , seg. PM is the median
• PM = 9cm
• $PQ ^ { 2 }$ + $PR ^ { 2 }$ = 290

To find -

• QR

Now, it is given that in ∆PQR , s.g .PM is the median. so, by using apollonius theorem.

$\Rightarrow$$PQ ^ { 2 }$ + $PR ^ { 2 }$ = $2PM ^ { 2 }$ + $2MR ^ { 2 }$

$\Rightarrow$ 290 = 2 × $9 ^ { 2 }$ + $2MR ^ { 2 }$

$\Rightarrow$ 290 = 162 + $2MR ^ { 2 }$

$\Rightarrow$ 128 = $2MR ^ { 2 }$

$\Rightarrow$ $MR ^ { 2 }$ = 64

$\Rightarrow$ MR = √64

$\Rightarrow$ MR = + 8cm

But we know that side can't be negative. so,

$\huge\mathfrak\orange\star$ MR = 8cm

Now , we know that,

$\Rightarrow$ QR = 2MR

$\Rightarrow$ QR = 2 × 8

$\Rightarrow$ QR = 16cm .