Question

Exercise 15.2
The area of a rhombus is 72 cm². If the perimeter is 32 cm, find its altitude.​

Answer 1

Given: The area of a rhombus is 72 cm². And the perimeter is 32 cm.

Need to find: The altitude of the rhombus.

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

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

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• Here, perimeter is given 32 cm. Comparing the formula with the perimeter.

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Therefore,

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$:\implies\sf 4 \times Side = 32 cm \\\\\\:\implies\sf Side = \cancel\dfrac{32}{4} \\\\\\:\implies{\underline{\boxed{\frak{\pink{Side = 8 \; m}}}}}$

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$\therefore{\underline{\sf{Hence,\;side\; of \; the \; rhombus \; is\: \bf{8\;m }.}}}$

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❒ Now, finding altitude of the rhombus.

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$\underline{\bf{\dag} \:\mathfrak{Using\: formula \: :}}$⠀⠀⠀⠀

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$\star\;\boxed{\sf{\purple{Area_{\:(rhombus)} = Side ⠀\times Altitude}}}$

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• Area of the rhombus is given which is 72 cm².

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Therefore,

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$:\implies\sf 72 = 8 \times Altitude \\\\\\:\implies\sf Altitude = \cancel\dfrac{72}{8} \\\\\\:\implies{\underline{\boxed{\frak{\purple{Altitude = 9\;cm}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; altitude\; of \; the \; rhombus\;is \;\bf{9\;cm }.}}}$

Answer 2

Answer:

Given :-

The area of a rhombus is 72 cm². And the perimeter is 32 cm.

To Find :-

Altitude

Solution :-

As we know that

Side of Rhombus = Perimeter/4

Side = 32/4

Side = 8 cm

Now,

Area of Rhombus = Side × Altitude

72 = 8 × Altitude

72/8 = Altitude

$\frak \pink{Altitude = 9 \: cm}$