Question

1. Find the length of OR in Figure 9.​

Answer 1

Step-by-step explanation:

In Triangle PTR , PR = 13 cm , TR = 5 cm

By Pythagoras Theorem,

(PR)^2 = (PT)^2 + (TR)^2

(13cm)^2 = (PT)^2 + (5cm)^2

169 cm^2 = (PT)^2 + 25 cm^2

(PT)^2 = 169 cm^2 - 25 cm^2

(PT)^2 = 144 cm^2

PT = √144 cm^2

PT = 12 cm

In Triangle PQT , PQ = 15 cm , PT = 12 cm

By Pythagoras Theorem,

(PQ)^2 = (PT)^2 + (QT)^2

(15cm)^2 = (12cm)^2 + (QT)^2

225 cm^2 = 144 cm^2 + (QT)^2

(QT)^2 = 225 cm^2 - 144 cm^2

(QT)^2 = 81 cm^2

QT = √81 cm^2

QT = 9 cm

QR = QT + TR = 9cm + 5cm = 14cm

Answer 2

Answer:

14 cm

Step-by-step explanation:

in ΔPTR

By pythagoreous triplet

PR² = TR²+PT²

(13)² = (5)² + PT²

169 = 25 +PT²

PT² = 169-25

PT² = 144

PT= √144

PT = 12 cm

in ΔPTQ

By pythagoreous triplet

QP² = QT²+ PT²

(15)² = QT² + (12)²

225 = QT² + 144

QT² = 225-144

QT = √81

QT = 9 cm

QR = QT + TR

QR = 9cm + 5 cm

QR = 14 cm