Question

1) If the area of a rhombus is 24 sq.cm and one of the diagonals is 8cm, the 1
length of its other diagonal is
*
○2cm
○8cm
○6cm
○3cm​

Answer 1

Answer:

4. 3cm

Step-by-step explanation:

Area of Rhombus= diagonal¹ × diagonal²

24 = 8 × diagonal²

24/8 = diagonal²

Therefore diagonal²=3cm

Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the Concept of Area of Rhombus has been used. We see that we are given one diagonal of the rhombus and its area. So we already know the formula of area of rhombus. We can apply values in the formula and get our answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Area\;of\;Rhombus\;=\;\bf{\dfrac{1}{2}\:\times\:D_{1}\:\times\:D_{2}}}}}$

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★ Solution :-

Given,

» Area of Rhombus = 24 cm²

» First diagonal of rhombus = D₁ = 8 cm

• Let the second Diagonal of the Rhombus be D₂.

Now we have the formula of Area of Rhombus.

$\\\;\sf{:\rightarrow\;\;Area\;of\;Rhombus\;=\;\bf{\dfrac{1}{2}\:\times\:D_{1}\:\times\:D_{2}}}$

By applying values, we get

$\\\;\sf{:\rightarrow\;\;24\;=\;\bf{\dfrac{1}{2}\:\times\:8\:\times\:D_{2}}}$

$\\\;\sf{:\rightarrow\;\;24\;=\;\bf{4\:\times\:D_{2}}}$

$\\\;\sf{:\rightarrow\;\;D_{2}\;=\;\bf{\dfrac{24}{4}}}$

$\\\;\bf{:\rightarrow\;\;D_{2}\;=\;\bf{\red{6\;\:cm}}}$

So option c.) 6 cm is correct.

$\\\;\underline{\boxed{\tt{Length\;\:of\;\:other\;\:Diagonal\;=\;\bf{\purple{6\;\:cm}}}}}$

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★ More to know about Rhombus :-

• Rhombus is a type of parallelogram.

• Opposite sides of Rhombus are equal and parallel.

• Diagonals of Rhombus bisect each other at 90°

• Alternative method to calculate the area of Rhombus ::

$\\\;\sf{\leadsto\;\;Area\;of\;Rhombus\;=\;Base\:\times\:Height}$