Question

what will be the answer

Answer 1

Hope my answer will help you :)

Answer 2

$\huge \boxed{ \bf{Question}}$

Rectangle ABCD is a rhombus diagonal BD=24cm,AB=13cm, length of the other diagonal AC is

a) 12cm. b)11cm. c)5cm. d)10cm.


$\huge \boxed{ \bf{Answer}}$

The correct answer is

$\implies \: (d) \: 10 \: cm$


$\boxed{ \bf{Explanation \: \div }}$


$\bf \underline {Given} \div$

ABCD is a rhombus.

AB = 13 cm, BD = 24 cm

To find : The length of diagonal AC.


$\bf \underline{Process} \div$

As ABCD is a rhombus so, it's diagonals bisect each other perpendicularly.

Therefore ,

$BO = DO = 12cm$

$AO= CO$

$\angle \: AOB = \angle BOC =\angle \:COD = \angle \: DOA \: = {90}^{0}$


Now,

In ∆AOB,

By using Pythagoras theorem

$= > \: {AB}^{2} = { BO }^{2} + { AO }^{2}$

$= > \: {13}^{2} = {12}^{2} + { AO }^{2}$

$= > { AO }^{2} = 169 - 144$

$= > { AO }^{2} = 25$

$= > \: AO \: = \sqrt{25}$

$= > AO = 5$


So we got,

AO = 5 cm.

Therefore , AC = 2(AO)

AC = 2 × 5

AC = 10 cm


So, the length of the other diagonal is

$\bf{10 \: cm}$