Question

find the perimeter of the rhombus if th
e lengths of the diagonals 1
2c



m,16cm respectively​

Answer 1

Explanation:

Rhombus

RhombusSolve for perimeter

RhombusSolve for perimeterP=2p2+q2

Answer 2

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Correct Question:-

• find the perimeter of the rhombus if the lengths of the diagonals 12cm,16cm respectively?

$\text{\large\underline{\red{Given:-}}}$

• Length of the diagonal =12cm and 16cm

$\text{\large\underline{\green{To Find }}}$

• The perimeter of the rhombus =?

$\text{\large\underline{\orange{Solution:-}}}$

$\red \bigstar\large\purple{ \bold{ \underline{ \underline{step \: by \: step \: explaination:- }}}}$

• Rhombus is a two dimensional shape with four equal sides and four angles which can or cannot

• be 90 degree , but opposite Angle are always same and both diagonal of a rhombus are perpendicular and bisect each other.

• Consider Shape ABCD and 0 is the intersecting point of both diagonals which is bisecting both diagonals ,and both diagonal are perpendicular to each other .

According to definition :-

$\begin{gathered}\\ \implies\large\sf{ AO=\dfrac{16}{2}=8cm}\end{gathered}$

$\begin{gathered}\\ \implies\large\sf{BO=\dfrac{12}{2}=6cm}\end{gathered}$

• So AOB is the right angled triangle.

By using Pythagoras theorem :-

• We can find the length of AB which is a side of rhombus .

$\begin{gathered} \\ \pink \bigstar\large \orange{ \bold{ \underline{ \underline{according \: to \: pythagoras \: theorem \: : }}}}\end{gathered}$

$\begin{gathered}\\ \implies\large\sf{(AB)^2=(BO)^2+(AO)^2} \\ \\ \implies\large\sf{AB=\sqrt{(6)^2+(8)^2 cm}} \\ \\ \implies\large\sf{AB=\sqrt{36+64cm}} \\ \\ \implies\large\sf{ AB=\sqrt{100cm} =10cm}\end{gathered}$

$\text{\large\underline{\purple{As we know that:-}}}$

• The perimeter of rhombus is equal to 4a where a is the length of rhombus .

• So, perimeter of rhombus = 4a

$\begin{gathered} \\ \implies \large \sf \: perimeter \: of \: rhombus \: = 4a\end{gathered}$

$\begin{gathered} \\ \implies \large \sf \: perimeter \: of \: rhombus \: = 4 \times 10cm\end{gathered}$

$\begin{gathered} \\ \implies \large \sf \: \: perimeter \: of \: rhombus \: = 40cm\end{gathered}$

Hence,

the side is 10cm and the perimeter of rhombus is 40cm.

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