Question

there are of a rhombus is 510 sq.cm if one of the diagonals is 34cm find the length of the other daigonal​

Answer 1

$\bf \: \underline{Given} \: :$ ↴

$\sf \: Area \: of \: the \: Rhombus \: = \: 510 \:sq.cm$

$\sf \: One \: of \: the \: diagonal \: of \: Rhombus \: = \: 34 \: cm$

$\bf \: \underline{To \: find }:$ ↴

$\sf \: We \: have \: to \: find \: the \: length \: of \: the \: another \: diagonal.$

$\bf \: \star \: \underline{ \: So \: Let's \: Start} \: \star$

$\sf \: Formula \: applied \: :$ ↴

$\boxed{\red{\star}\ \; \pink{\sf Area=\dfrac{1}{2}\times (D_1 \: \times \: D_2)}}$

$\bf \: Where,$

$\sf \: \bull \:D_1 \: denotes \: Diagonal \: 1$

$\sf \: \bull \: D_2 \: denotes \: Diagonal \: 2$

$\sf \:Now,$

$\sf \: Area\: of \:the \:rhombus \:= \:60\: sq.cm$

$\sf \:Length \:of \:Diagonal \:1 \:=\: 34\: cm$

$\sf \:Length \:of \:Diagonal \: 2 \: = \: D_2 \:cm$

$\sf \: \underline{Putting \: values} :$

$\longrightarrow\ \; \sf Area=\dfrac{1}{2}\times (34 \: \times \: D_2)$

$\longrightarrow \ \; \sf 510=\dfrac{1}{2}\times 34D_2$

$\longrightarrow \ \; \sf 510= 17D_2$

$\sf \longrightarrow \: D_2 \: = \: \dfrac{510}{17}$

$\sf \longrightarrow \: D_2 \: = \: 30\: cm$

$\sf \longrightarrow Answer \: = \:30\:cm$

$\pink{ \sf \: So, \: the \: length \: of \: D_2 \: = \: 30\: cm }$

Answer 2

Given :

• Area of Rhombus = 510cm²
• One Diagonal of Rhombus = 34cm

To Find :

• Second Diagonal of the Rhombus.

Solution :

✰ As we know that, Area of Rhombus is given by ½ × (Product of its diagonal) or ½ × (D1 × D2). Now in this Question it is given that area of Rhombus is 510cm² and one Diagonal is 34cm and we have to find the second Diagonal of the Rhombus. So Simply we will put the given values in the formula to find the second Diagonal of the Rhombus.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀Area = ½ × (D1 × D2)

⠀⠀⠀⟼⠀⠀⠀510 = ½ × (34 × D2)

⠀⠀⠀⟼⠀⠀⠀510 × 2 = 34 × D2

⠀⠀⠀⟼⠀⠀⠀1020 = 34 × D2

⠀⠀⠀⟼⠀⠀⠀1020 / 34 = D2

⠀⠀⠀⟼⠀⠀⠀30 = D2

⠀

Verification :

⠀⠀⠀⟼⠀⠀⠀Area = ½ × (34 × 30)

⠀⠀⠀⟼⠀⠀⠀Area = ½ × 34 × 30

⠀⠀⠀⟼⠀⠀⠀Area = 34 × 15

⠀⠀⠀⟼⠀⠀⠀510 = 510

Hence Verified

Thus Second Diagonal of Rhombus is 30cm

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