Question

Find the length of QR in Figure 9
​

Answer 1

Answer:

14cm

Step-by-step explanation:

Step 1

Using Pythagoras find PT (altitude) for triangle PTR

PT =

$\sqrt{13 {}^{2} - 5 {}^{2} }$

= 12.

Step 2

For triangle PQT which is also a right angled traingle again use Pythagoras to find QT.

QT =

$\sqrt{15 {}^{2} - 12 {}^{2} }$

= 9

Step 3

Finally add QT and RT to get QR

= 9 + 5

= 14cm

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

♣ In ∆PTR , right angled at T.

By Pythagoras theorem,

Hypotenuse² = base² + height²

➛ 13² = 5² + PT²

➛ PT² = 13² - 5²

➛ PT² = 169 - 25

➛ PT² = 144

➛ PT = 12cm

▬▬▬▬▬▬▬▬▬▬▬▬

Now , ♣

In ∆PTQ ,

By Pythagoras theorem,

➛ QP² = QT² + PT²

➛ 15² = QT² + 12²

➛ QT² = 15² - 12²

➛ QT² = 225 - 144

➛ QT² = 81

➛ QT = 9cm

From figure ,

➠ QR = QT + TR

➠ QR = 9 + 5

➠ QR = 14cm

Hence , QR = 14cm