Question

In triangle PQR, QD is an altitude. If QD is 15 cm and PR is 34, find PQ​

Answer 1

Answer:

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Step-by-step explanation:

From the figure, we have QR=QT+TR.

To find : QT and TR.

In the right angled triangle PTQ,

∠PTQ=90o [PT is attitude]

By Pythagoras Theorem, PQ2=PT2+QT2

∴PQ2−PT2=QT2

∴QT2=252−152=625−225=400 ...(1)

Similarly, in the right angled triangle PTR,

by Pythagoras Theorem, PR2=PT2+TR2

∴TR2=PR2−PT2

=172−152

=289−225=64

TR=64=8cm  ...(2)

From (1) and (2)

QR = QT + TR = 20 + 8 = 28 cm.

Answer 2

Answer:

2.67 cm.

Step-by-step explanation:

In triangle PQR,

PD = DR = 34/2 = 17 cm.[Since QD is the altitude of PQR]

Therefore in Triangle QDR,

According to the Pythagoras Theorem,

(QR)^2 = (QD)^2 + (DR)^2

=> (QR)^2 = (15)^2 + (17)^2

=> QR^2 = 225 + 289

=> QR^2 = 514

=>QR = 22.67 cm. [Ans]