Question

In the figure angle PSQ=90°,PQ=10cm,QS=6cm and RQ=9cm. Calculate the length of PR. Question No. - 3
​

Answer 1

$\huge\underline\mathcal{Solution!!...}$

$\green{\underline\textbf{Given...}}$

angle PSQ = 90°

PQ = 10cm

QS = 6cm

RQ = 6cm

$\green{\underline\textbf{</strong><strong>T</strong><strong>o</strong><strong> </strong><strong>find</strong><strong>...}</strong><strong>}</strong><strong>$

length of PR = ?

$\green{\underline\textbf{</strong><strong>l</strong><strong>n</strong><strong> </strong><strong>trian</strong><strong>gle</strong><strong> </strong><strong>PSQ</strong><strong>.</strong><strong>.</strong><strong>.</strong><strong>}</strong><strong>}</strong><strong>$

$\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{\underline\textbf{</strong><strong>U</strong><strong>sing</strong><strong> </strong><strong>Pythagoras</strong><strong> </strong><strong>the</strong><strong>orem</strong><strong> </strong><strong>to</strong><strong> </strong><strong>find</strong><strong> </strong><strong>PS</strong><strong>.</strong><strong>.</strong><strong>.</strong><strong>}</strong><strong>}$

• PQ² = QS² + PS²

10² = 6² + PS²

100 = 36 + PS²

√64 = PS

• : 8cm = PS

$\red{\underline\textbf{the length of PS is 8cm...}}$

===>

$\green{\underline\textbf{In triangle PRS...}}$

PS = 8cm

RS = RQ + QS

= 9cm + 6cm

= 15cm

$\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{\underline\textbf{</strong><strong>U</strong><strong>sin</strong><strong>g</strong><strong> Pythagoras</strong><strong> theorem</strong><strong> to</strong><strong> find</strong><strong> </strong><strong>PR</strong><strong>...}</strong><strong>}</strong><strong>$

• PR² = PS² + RS²

PR² = 8² + 15²

PR² = 64 + 225

PR = √289

• : PR = 17cm

$\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{\underline\textbf{</strong><strong>T</strong><strong>here</strong><strong>fore</strong><strong>,</strong><strong>the</strong><strong> </strong><strong>leng</strong><strong>th</strong><strong> </strong><strong>of</strong><strong> </strong><strong>PR</strong><strong> </strong><strong>is</strong><strong> </strong><strong>1</strong><strong>7</strong><strong>c</strong><strong>m</strong><strong>...}</strong><strong>}</strong><strong>$

-----------------------------

Thanks!!...❣️✌️

-----------------------------

Answer 2

Answer:

PR=157

By phythagorous theorem

hypo2 = s12 +s22

PQ2 = QS2 + PS2

10^2 = 6^2 +PS^2

100 = 36 + PS^2

PS2 = 36 - 100

PS2 = 64

PS = 8

Sum of all angles of a triangle is

PS+RS+PR=180

8+15+PR=180

23+PR=180

PR=180-23

PR=157

ans=157=PR hope it helps