Question

IF angle PQR = 90°, O is the centroid, PQ = 5 cm and QR = 12 cm. Find the value of OQ.


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Answer 1

Answer :-

Value of OQ is 4 1/3 cm.

Explanation :-

Given

• PQ = 5 cm

• QR = 12 cm

• ∠PQR = 90°

O is the centroid

Consider Δ PQR

In Δ PQR, ∠PQR = 90°

∴ Δ PQR is Right - angled triangle

By Pythagoras theorem

PR² = PQ² + QR²

⇒ PR² = (12)² + (5)²

⇒ PR² = 144 + 25

⇒ PR² = 169

⇒ PR = √169

⇒ PR = 13

O is the centroid

Centroid intersects the median

∴ QM is the median to hypotenuse.

We know that

In a Right - angled triangle, median to hypotenuse is half the the length of the hypotenuse.

⇒ QM = PR/2

⇒ QM = 13/2 cm

[ ∵ PR = 13/2 cm ]

We know that

Centroid of a triangle is intersection of 3 medians and divides median in 2 : 1 ratio in another words, OQ = (2/3) of QM

⇒ OQ = (2/3) of QM

⇒ OQ = (2/3) * QM

⇒ OQ = (2/3) * (13/2)

[ ∵ QM = 13/2 ]

⇒ OQ = (2 * 13)/(3 * 2)

⇒ OQ = 13/3

⇒ OQ = 4 1/3 cm

∴ the value of OQ is 4 1/3 cm.