Question

Diagonals of rhombus are 15 cm and 20 cm. Then its area and perimeter are :
(A) 150 cm2, 50 cm
(B) 120 cm?, 50 cm
(C) 150 cm?, 70 cm
(D) 120 cm, 70 cm​

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

FORMULA :-

• Area = 1/2 × d1 × d2

= 1/2 × 15 × 20

= 15 × 10

= 150 cm²

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FORMULA :-

• √d1² + d2² / 2

= √15² + 20² / 2

= √225 + 400 /2

= √625 / 2

= 25 / 2

= 25 / 2 × 4

= 50 cm.

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∴ Option ( a ) 150 cm², 50 cm