Question

If diagonal of rectangle is 26 cm and one of the side is 24cm then find the other side ?

Answer 1

Answer:

Step-by-step explanation:

rectangle is making two right angeled  triangle when we draw one diagonal.

hence using P. G. Theorem,

(diagonal)² = (one side of rectangle)² + (other  side of rectangle)²

(26)²  =  (24)²  +  (other side of rectangle)²

(other side of rectangle)²  =  (26)²  -  (24)²

(other side of rectangle)²  =  676  -  576

(other side of rectangle)²  =  100  =   10²

√(other side of rectangle) = √10

(other side of rectangle)    = 10cm

Answer 2

GIVEN :-

• Diagonal of Rectangle is 26 cm.
• One side of Rectangle is 24 cm.

TO FIND :-

• The length of other side.

SOLUTION :-

$\underline{ \bigstar \: \textsf{Diagram.}}$

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\tt\large{A}}\put(7.7,1){ \tt\large{B}}\put(9.5,0.7){\sf{\large{24 cm}}}\put(11.5,1){ \tt\large{C}}\put(8,1){\line(1,0){3.5}}\put(8,1){\line(0,2){2}}\put(11.5,1){\line(0,3){2}}\put(8,3){\line(3,0){3.5}}\put(8.8,2){\sf{\large{26 cm}}}\qbezier(8,1)(8,1)(11.5,3)\put(11.5,3){ \tt\large{D}}\put(11.3,1){\line(0,2){0.2}}\put(11.3,1.2){\line(2,0){0.2}}\end{picture}$

$\underline{\bigstar \: \sf{In\: \triangle \; BCD \: by \: pythagoras \: theorem}}$

$: \implies \displaystyle \sf \: (DB)^{2} = (BC)^{2} + (DC)^{2}$

$: \implies \displaystyle \sf \: (26) ^{2} = (24) ^{2} + (DC)^{2}$

$: \implies \displaystyle \sf \:676 = 576 + (DC)^{2}$

$: \implies \displaystyle \sf \: (DC)^{2} = 676 - 576$

$: \implies \displaystyle \sf \: (DC)^{2} =100$

$: \implies \displaystyle \sf \: DC= \sqrt{100}$

$: \implies \underline{ \boxed{\displaystyle \sf \: DC=10 \: cm}}$

$\therefore \underline{ \displaystyle \sf length \: of \: other \: side\: DC \:is \: 10 \: cm. }$