Question

the diagonals of a rhombus are in the ratio 3"4. if the longer diagonal is 12cm, then find the area of the rhombus

Answer 1

Answer:

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Answer 2

• The diagonals of a rhombus are in ratio 3:4 .

1. If the longer diagonal is 12cm .

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• The area of the rhombus .

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Let,

• The smaller diagonal of the rhombus be '3a' .
• And the longer diagonal of the rhombus be '4a' .

☯︎ According to the question,

$⇒ 4a = 12 \\ </p><p></p><p>⇒ a = \rm{\dfrac{12}{4}} \\ </p><p></p><p> </p><p> </p><p></p><p>⇒ a = 3 cm</p><p>$

✞︎ Hence the smaller diagonal of the rhombus is

$⟹ 3a \\ </p><p></p><p>⟹ 3 × 3 \\ </p><p></p><p>⟹ 9 cm</p><p>$

☞︎︎︎ We know that,

$\begin{gathered}\bigstar\:\bf{\red{\overbrace{\underbrace{\red{Area\:of\:rhombus\:=\:\dfrac{1}{2}\times{d_1}\times{d_2}\:}}}}} \\\end{gathered} </p><p>★ </p><p>$

⇛ Area of the rhombus = 9 × 6

⇛ Area of the rhombus = 54 cm²

$\huge\red\therefore$The area of the rhombus is '54 cm