Question

if the diagonals of a rhombus of lengths 24cm and 18cm . find the length of the side of the rhombus and hence find its perimeter.......
pls give an explanation.......
best explained and correct answer will be marked as the brainliest.......​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Side\:of\:Rhombus=15\:cm}}$

${\bold{\therefore Perimeter\:of\:Rhombus=60\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline\bold{Given : } \\ \implies Diagonal (D_{1}) = 24 \: cm \\ \\ \implies Diagonal (D_{2}) = 18\: cm \\ \\ \underline\bold{To \: Find : } \\ \implies Side \:of \: Rhombus = ?\\\\\implies Perimeter\:of\:Rhombus=?$

• According to given question :

$\bold{Rhombus \: Property : } \\ \implies Diagonals \: bisect \: each \: other \: at \: 90 \degree \\ \\ \implies All \: side \: of \: rhombus \: are \: equal \\ \\ \bold{Let \: ABCD\: is \: a \: Rhombus \: and \: point \: O \: }\\ \bold{Where \: both \: Diagonals \: bisect \: each \: other}\\ \\ \implies AO = CO = 8 \: cm \\ \\ \implies BO = DO = 12 \: cm \\ \\ \bold{In \: \: Right \: angle \: \triangle \: AOB} \\ \implies {AB}^{2} = {AB}^{2} + {BO}^{2} \\ \\ \implies {AB}^{2} = {9}^{2} + {12}^{2} \\ \\ \implies AB = \sqrt{81 + 144} \\ \\ \implies AB= \sqrt{225} \\ \\ \implies \bold{AB= 15 \: cm} \\ \\ \bold{\therefore Side \: of \: Rhombus \: is \: 15 \: cm}\\\\\bold{For\:finding\:perimeter:}\\\\\implies Perimeter\:of\:Rhombus=4\times side\\\\\implies Perimeter=4\times 15\\\\\bold{\implies Perimeter=60\:cm}\\\\\bold{\therefore Perimeter\:of\:Rhombus=60\:cm}$

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Half of the diagonal of 18 and 24 is 9 and 12

So , by Pythagoras theorem we get ,

$\sf \to {h}^{2} = {b}^{2} + {p}^{2} \\ \\ \sf \to</p><p> {h}^{2} = {(9)}^{2} + {(12)}^{2} \\ \\ \sf \to</p><p> {h}^{2} = 225 \\ \\ \sf \to </p><p>h = 15 \: cm$

Therefore , length of each side of the rhombus is 15 cm

We know that ,

$\large\fbox{ \sf \fbox{ Perimeter \: of \: rhombus = 4 × sides }}$

$\to \sf Perimeter = 4 × 15 \\ \\ \to \sf</p><p>Perimeter = 75 \: cm$

Therefore , the perimeter of the given rhombus is 75 cm