Question

Find the length of the diagonal of a
rectangle PORS whose length and breadth
are 24 m and 7 m, respectively,​

Answer 1

GIVEN :-

• length of rectangle = 24 m
• breath of rectangle = 7 m

TO FIND :-

• diognal of rectangle

SOLUTION :-

in rectangle PQRS

length = PQ = RS = 24 m

breath = QR = PS = 7 m

diognal = QS = PR = ?

now we have to finds QS

if we see , then QSR is a right angled triangle

( as angle QSR is 90° due to rectangle )

so in ∆ QSR

QR = 7 m

RS = 24 m

now we know according to pythogoras theorem

$\implies \boxed{ \rm{ {h}^{2} = {p}^{2} + {b}^{2} }}$

where

h = hypotenuse

p = perpendicular

b = base

similarly ,

$\implies \rm{ {QS}^{2} = {QR}^{2} + {RQ \: }^{2} }$

$\implies \rm{ {QS}^{2} = {(24)}^{2} + {(7)\: }^{2} }$

$\implies \rm{ {QS}^{2} = 576 + 49 }$

$\implies \rm{ {QS}^{2} = 625 }$

$\implies \rm{ \sqrt{{QS}^{2} \: \: } = \sqrt{625 \: \: }}$

$\implies \rm{ QS = 25 \: m}$

HENCE ,

$\implies \boxed{ \boxed{ \rm{diognal \: of \: rectangle = 25 \: m}}}$

[ note : we can even solve this question by using direct formula d = √( l² + b² ) where d = diognal , l = length and b = breath ]