Question

The perimeter of a rhombus is 150 cm and one of its diagonal is 45 cm find the length of the Other diagonal and the area of Rhombus

Answer 1

Solution :

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

• The perimeter of rhombus = 150 cm
• It's one diagonal = 45 cm

Show Diagram :

$\setlength{\unitlength}{1.3cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large\sf{A}}\put(9,1.3){\sf{}}\put(9.9,1.3){\sf{45\:cm}}\put(7.7,0.9){\large\sf{B}}\put(9.2,0.7){\large\sf{?cm}}\put(11.1,0.9){\large\sf{C}}\put(9.9,2.1){\large\sf{O}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(11,1){\line(-1,1){2}}\put(8,1){\line(2,1){4}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large\sf{D}}\end{picture}$

$\underline{\bf{Explanation\::}}}}$

$\bigstar$ Firstly, we get side of Rhombus :

$\underline{\sf{Perimeter\:of\:Rhombus\::}}}$

$\longrightarrow\sf{Perimeter\:_{(rhombus)}=4\times Side}\\\\\longrightarrow\sf{150\:cm=4\times Side}\\\\\longrightarrow\sf{Side=\cancel{150/4}cm}\\\\\longrightarrow\bf{Side=37.5\:cm}$

We know that formula to get another diagonal of rhombus :

$\boxed{\bf{Diagonal\:(d_2)=\sqrt{4a^{2}-d_{(1)}{2} } }}}$

$\longrightarrow\sf{Diagonal\:(d_2)=\sqrt{4\times(37.5)^{2} -(45)^{2} } }\\\\\longrightarrow\sf{Diagonal\:(d_2)=\sqrt{4\times 1406.25-2025} }\\\\\longrightarrow\sf{Diagonal\:(d_2)=\sqrt{5625-2025}} \\\\\longrightarrow\sf{Diagonal\:(d_2)=\sqrt{3600} }\\\\\longrightarrow\bf{Diagonal\:(d_2)=60\:cm}$

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$\underline{\sf{\bigstar\:\:Area\:of\:Rhombus\::}}$

$\longrightarrow\sf{Area\:_{(rhombus)}=\dfrac{1}{2} \times (diagonal)_1\times (diagonal)_2}\\\\\\\longrightarrow\sf{Area\:_{(rhombus)}=\dfrac{1}{\cancel{2}} \times 45\:cm \times \cancel{60}\:cm}\\\\\\\longrightarrow\sf{Area\:_{(rhombus)}=(45\times 30)cm^{2} }\\\\\\\longrightarrow\bf{Area\:_{(rhombus)}=1350\:cm^{2} }$