Question

The area of a rhombus is 16 cm2 and the length of one of its diagonal is 4 cm. Calculate the side and perimeter

Answer 1

Answer:

side = 4cm

perimeter 16 cm

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Answer 2

$\begin{gathered}\bf Given\begin{cases} & \sf{area\:of\;rhombus = \bf{16\;cm²}} \\ & \sf{length\;of\;one\;of\;its\;diagonal = \bf{4\;cm}} \end{cases}\\ \\\end{gathered}$

to find:-

• Length of other diagonal.

$\begin{gathered}\bigstar \underline{\underline{\mathfrak{Solution:-}}}\\\end{gathered}$

$\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}$

$\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(rhombus)} = frac{1}{2}(product of diagonals)}}}}\\ \\\end{gathered}$

☯ Let another diagonal be x

$\begin{gathered}{\underline{\sf{\bigstar\: According\:to\:the\:question\::}}}\\ \\\end{gathered}$

$\begin{gathered}:\implies \sf Area=\frac{1}{2} \times (x)(4)\\\\:\implies 16=\frac{1}{2} \times (x)(4)\\\\:\implies 16 = 2x\\\\:\implies x=\frac{16}{2} =8\\\\:\implies \sf \boxed{\boxed{\bold{x=8cm.}}}\\\\\end{gathered}$

• Therefore, length of another diagonal is 8cm.

_______________________

$\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: More\:to\:know :}}}}}\mid}\\\\\end{gathered}$

$\sf properities\:of\:rhombus:-$

$\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(rhombus)} = frac{1}{2}(product of diagonals)}}}}\\ \\\end{gathered}$

$\begin{gathered}\star\;{\boxed{\sf{\pink{perimeter_{\;(rhombus)} = (4 \times sides)}}}}\\ \\\end{gathered}$

• $\sf number\:of\:edges = 4$

• $\sf Number\:of\:vertices = 4$