Question

Area of a rhombus is 252 and one of the diagonals is 14 cm

Answer 1

Step-by-step explanation:

$\sf \: i \: think \: u \: want \: other \: diagonal \: of \: rhombus$

$\sf \: area \: of \: rhombum \: = 252 \: {cm}^{2}$

$\sf \: first \: diagonal(d1) = 14$

$\sf \: let \: second \: diagonal \: is\:( d2)$

$\sf \: area \: = 252 \: \: \: \: \: \\ \sf \: d1 \times d2 = 252$

$\sf \: d2 = \frac{252}{14}$

$\sf \: d2 = 18 \: cm$

Answer 2

Correct Question :-

• If Area of a rhombus is 252cm² and one of the diagonals is 14 cm then find the other diagonal .

Given :-

• Area of Rhombus = 252cm²
• First Diagonal ( D1 ) = 14cm

To Find :-

• Second Diagonal of the Rhombus .

Solution :-

Let Second Diagonal be D2

$\quad {:} \longrightarrow \sf\boxed{\bf{Area \: of \: Rhombus \:= \: \dfrac{1}{2} \: \times \: (Product \: of \: Diagonals) }}$

$\quad {:} \longrightarrow \sf{\sf{252 \:= \: \dfrac{1}{2} \: \times \: (14 \: \times \: D2) }}$

$\quad {:} \longrightarrow \sf{\sf{252 \:= \: \dfrac{1}{\cancel2} \: \times \: \cancel{14} \: \times \: d2 }}$

$\quad {:} \longrightarrow \sf{\sf{252 \:= \: 7 \: \times \: d2 }}$

$\quad {:} \longrightarrow \sf{\sf{ \cancel\dfrac{252}{7} \:= \: d2 }}$

$\quad {:} \longrightarrow \sf{\bf{ 36\:= \: Second \: Diagonal }}$

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So, Second Diagonal = 36cm

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Verification :-

$\longmapsto \sf\boxed{\bf{Area \: of \: Rhombus \:= \: \dfrac{1}{2} \: \times \: (Product \: of \: Diagonals) }}$

$\longmapsto \sf{\sf{252 \:= \: \dfrac{1}{2} \: \times \: 14 \: \times \: 36 }}$

$\longmapsto \sf{\sf{252 \:= \: \dfrac{1}{2} \: \times \: 504 }}$

$\longmapsto \sf{\sf{252 \:= \: \dfrac{1}{\cancel2} \: \times \: \cancel{504} }}$

$\longmapsto \sf{\bf{252 \:= \: 252 }}$

Hence, Proved

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