Question

If the diagonals of a rhombus 10cm and 24cm.Find the perimeter.

Answer 1

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.3cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(9,1.3){\sf{5 cm}}\put(9.9,1.3){\sf{12 cm}}\put(7.7,0.9){\large{B}}\put(9.2,0.7){\sf{\large{? cm}}}\put(11.1,0.9){\large{C}}\put(9.9,2.1){\large{O}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(11,1){\line(-1,1){2}}\put(8,1){\line(2,1){4}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\end{picture}$

$\rule{120}{1}$

• Let AC and BD be the Diagonal of Rhombous ABCD of measurement 24 cm and 10 cm.
• Diagonals of rhombous Bisect each other, hence OB = 5 cm & OC = 12 cm.

• we know that there will be 90° at the Midpoint of Rhombous, and thus create Right Angle Triangle OBC.
• By Using Pythagoras Formula or Pythagorean Triplet, we can Find the value of Side of Rhombous i.e. BC

$\begin{tabular}{|c |c | c|}\cline{1-3}p/b & b/p & h \\\cline{1-3}3 & 4 & 5 \\5 & 12 &13\\8 & 15&17 \\7 & 24&25\\\cline{1-3}\end{tabular}$

• From the above triplet box, we get that OB = 5 cm, OC = 12 cm, BC = 13 cm

$\rule{180}{2}$

$\underline{\bigstar\:\:\textsf{Perimeter of Rhombous :}}$

$\dashrightarrow\sf\:\: Perimeter_{(Rhombous)}=4 \times Side\\\\\\\dashrightarrow\sf\:\:Perimeter_{(Rhombous)}=4 \times BC\\\\\\\dashrightarrow\sf\:\:Perimeter_{(Rhombous)}=4 \times 13\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{\textbf{Perimeter _{\textbf{(Rhombous)}} = 52 cm}}}}$