Question 6 S is any point on side QR of a - P QR- Show that PQ - QR - RP -2 PS-

Given in Δ PQR, S is any point on side QR In Δ PQS, PQ +QS gt;PS [sum of two sides of a trianlge is greater than the third side] Similarly, in Δ PRS, SR +P ...

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Standard IX

Mathematics

Right Angled Triangle

Question 6 S ...

Question

Question 6
S is any point on side QR of a $Δ P Q R$ . Show that PQ + QR + RP > 2 PS.

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Solution

Given in $Δ P Q R$ , S is any point on side QR

$I n Δ P Q S, P Q + Q S > P S$
[sum of two sides of a trianlge is greater than the third side]
$S i m i l a r l y, i n Δ P R S, S R + P R > P S$
[sum of two sides of a triangle is greater than the third side]
on adding Eqs (i) and (ii). we get,
$P Q + Q S + S R + R P > 2 P S$
$\Rightarrow P Q + (Q S + S R) + R P > 2 P S \Rightarrow P Q + Q R + R P > 2 P S [∵ Q R = Q S + S R]$

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Question 6 S is any point on side QR of a ΔPQR. Show that PQ + QR + RP > 2 PS.

Question 6
S is any point on side QR of a $Δ P Q R$ . Show that PQ + QR + RP > 2 PS.