Question

Rationalise the denominator of 3+2√3 / 3-2√3 and simplify​

Answer 1

Given: Diagonals of Rhombus are 15 cm and 20 cm.

To find: Area and Perimeter of the rhombus.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀

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$\star\;\boxed{\sf{\pink{Area_{\:(rhombus)} = \dfrac{1}{2} \times d_{1} \times d_{2}}}}$

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Where

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$\sf d_1$ and $\sf d_2$ are the Diagonals of the rhombus.

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Therefore,

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$:\implies\sf Area_{\:(rhombus)} = \dfrac{1}{2} \times 15 \times 20 \\\\\\:\implies\sf Area_{\:(rhombus)} = \dfrac{1}{\cancel{\;2}} \times 15 \times \;\cancel{20} \\\\\\:\implies\sf Area_{\:(rhombus)} = 15 \times 10 \\\\\\:\implies{\underline{\boxed{\frak{\pink{Area_{\:(rhombus)} = 150\;cm^2}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; area\; of \; the \; rhombus\; is\; \bf{ 150\;cm^2}.}}}$

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As We know that, To calculate side of the rhombus formula is given by :

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$\star\;\boxed{\sf{\purple{Side_{\:(rhombus)} = \dfrac{\sqrt{(d_{1})^2 + (d_{2})^2}}{2}}}}$

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We're given with both Diagonals, first diagonal is 15 cm and Second diagonal is 20 cm.

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Therefore,

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$:\implies\sf Side_{\:(rhombus)} = \dfrac{\sqrt{(15)^2 + (20)^2}}{2} \\\\\\:\implies\sf Side_{\:(rhombus)} = \dfrac{\sqrt{225 + 400}}{2} \\\\\\:\implies\sf Side_{\:(rhombus)} = \dfrac{\sqrt{625}}{2} \\\\\\:\implies{\underline{\boxed{\frak{\purple{ Side_{\:(rhombus)} = \dfrac{25}{2}}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \; side \; of \; the \; rhombus\; is \;\bf{\dfrac{25}{2} }.}}}$

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$\star\;\boxed{\sf{\blue{ Perimeter_{\:(rhombus)} = 4 \times Side}}}$

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Therefore,

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$:\implies\sf Perimeter_{\:(rhombus)} = \dfrac{25}{\cancel{\;2}} \times \cancel{\;4} \\\\\\:\implies\sf Perimeter_{\:(rhombus)} = 25 \times 2 \\\\\\:\implies{\underline{\boxed{\frak{\blue{Perimeter_{\:(rhombus)} = 50\; cm}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \; perimeter\; of \; the \; rhombus\; is \;50\;cm\; \bf{Option\;a) }.}}}$

Answer 2

Answer:

Choose as your wish

Step-by-step explanation:

Rationalize by 3 + 2√3

3+2√3 / 3-2√3  x 3 + 2√3 /3 +2√3

=  (3 + 2√3 )²/ (3)² - (2√3 )²

=  9 + 12 + 12√3/ 9-12

=  - (18 +12√3)/3

rationalize by 3 - 2√3

3+2√3 / 3-2√3  x 3 - 2√3 /3  -2√3

       (3)² - (2√3 )² / (3 + 2√3 )²

     = 9- 12/ 9 + 12 + 12√3

     =     -3 / 18 +12√3