Question

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

Answer 1

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`

`\therefore`Perimeter of the rectangle is 20cm.