Question

the peremeter of the rhombus is 20 cm. one of it diagnal is 8 cm. find the area of rhombus and length of other diagnal .

please it is very urgent

Answer 1

Answer:

Given, Perimeter of a rhombus = 20 cm

Perimeter of a rhombus = 4*side

Hence, side = 20/4 = 5 cm.

Now, we know that the diagonals of a rhombus bisect each other at right angles (90 degree).

Hence 'a right angled triangle can be visualised with 'side' as the hypotenuse'.

diagonal length = 8 cm

Half the length (since diagonal bisects each other) = 8/2 = 4 cm

(d/2)^2 + (d1/2)^2 = 5^2

4^2 + (d1/2)^2 = 5^2

(d1/2)^2 = 9

d1/2 = 3

d1 = 3*2 = 6 cm

Hence other diagonal = 6 cm.

Area = 1/2 * d1*d = 1/2 * 8 * 6 = 24 cm^2

Hope it helps!

Answer 2

$\underline{\underline{\bf{\bigstar\: Figure : }}}$

$\:\:$

$\setlength{\unitlength}{1.6mm}\begin{picture}(5,6)\put(0,0){\line(1,1){12}}\put(20,0){\line(1,1){12}}\put(0,0){\line(1,0){20}}\end{picture}\put(6.9,12){\line(1,0){20}}\put(15,0){\line(-2,3){8}}\put(5,3){}\put(4.5,-2){}\put(11,7.5){8 cm}$

$\:\:$

$\underline{\underline{\bf{\bigstar\: Given : }}}$

$\:\:$

• $\footnotesize{\red{ Perimeter\: of\: rhombus = 20cm}}$
• $\footnotesize{\red{ 1st\:Diagonal\: of\: rhombus = 8cm }}$

$\:\:$

$\underline{\underline{\bf{\bigstar\: To\: Find : }}}$

$\:\:$

• $\footnotesize{\red{ 2nd\:Diagonal\: of\: rhombus }}$

$\:\:$

$\underline{\underline{\bf{\bigstar\: Solution : }}}$

$\:\:$

$\footnotesize{\blue{ Perimeter\: of\:rhombus = side \times 4 }}$

$\footnotesize{\blue{\implies 20\:cm = side \times 4 }}$

$\footnotesize{\blue{\implies \dfrac{20\:cm}{4} = side }}$

$\footnotesize{\blue{\implies 5cm = side }}$

$\:\:$

$\rule{250}3$

$\:\:$

$\footnotesize{\green{ Area\: of\: rhombus = \dfrac{1}{2}d \sqrt{ {4a}^{2} - {d}^{2}} }}$

$\footnotesize{\green{\implies Area\: of\: rhombus = \dfrac{1}{2} \times 8cm \sqrt{ {(4 \times 5cm)}^{2} - {(8cm)}^{2}} }}$

$\footnotesize{\green{\implies Area\: of\: rhombus = \dfrac{1}{\cancel{2}} \times \cancel{8cm} \sqrt{ {(20cm)}^{2} - {64cm}^{2}} }}$

$\footnotesize{\green{\implies Area\: of\: rhombus = 4cm \sqrt{ {400cm}^{2} - {64cm}^{2}} }}$

$\footnotesize{\green{\implies Area\: of\: rhombus = 4cm \sqrt{ {336cm}^{2}} }}$

$\footnotesize{\green{\implies Area\: of\: rhombus = 4cm \times 18.33cm}}$

$\footnotesize{\green{\implies \dfrac{{d}_{1} \times {d}_{2}}{2} = {73.32cm}^{2} }}$

$\footnotesize{\green{\implies \dfrac{ 8cm \times {d}_{2}}{2} = {73.32cm}^{2} }}$

$\footnotesize{\green{\implies 8cm \times {d}_{2} = {73.32cm}^{2} \times 2 }}$

$\footnotesize{\green{\implies 8cm \times {d}_{2} = {146.64cm}^{2} \times 2 }}$

$\footnotesize{\green{\implies {d}_{2} = \dfrac{ {146.64cm}^{2}}{8\:cm} }}$

$\footnotesize{\green{\implies {d}_{2} = 18.33cm }}$