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The diagonals of a rhombus measures 6cm and 8cm, what is the perimeter of this rhombus?

User Muhamed
by
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1 Answer

3 votes

Diagram:-


\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4)\qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}

Required Answer:-

The diagonals of the Rhombus= d1 & d2=6cm and 8cm

Let the Side=a

As we know that in a Rhombus


{\boxed{\sf side=\sqrt {\left ({(d1)/(2)}\right)^2+\left ({\frac {d2}{2}}\right)^2}}}

  • Substitute the values


{:}\longmapsto
\sf a=\sqrt {\left ({\frac {6}{2}}\right)^2+\left ({\frac {8}{2}}\right)^2 }


{:}\longmapsto
\sf a=\sqrt {(3)^2+(4)^2}


{:}\longmapsto
\sf a=\sqrt {9+16}


{:}\longmapsto
\sf a=√(25)


{:}\longmapsto
\sf a=5cm

_____________

Again

we know that in a Rhombus


\boxed{\sf Perimeter=4a}

  • Substitute the values


{:}\longmapsto
\sf Perimeter=4×5


{:}\longmapsto
\sf Perimeter=20cm


\thereforePerimeter of the rectangle is 20cm.

User Confused Windbell
by
8.6k points

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