Question

the area of rhombus is 10cm one of its diagnol is 4cm find the length of the other diagnol
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Answer 1

If the diagonals of a rhombus are D1 and D2 then

area of rhombus = ½×D1×D2

10cm² = ½×4×D2

D2 = 10×2/4 = 20/4 = 5cm

Therefore the length of the other diagonal is 5cm

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Answer 2

$\large\underline\pink{Given:-}$

• Area of the Rhombus is 10 cm²
• And one of its diagonal is 4 cm.

$\large\underline\pink{To find:-}$

• Find the of the other diagonal of the Rhombus ....?

$\large\underline\pink{Solutions:-}$

• Let the one diagonal be 4 cm.
• Let the other diagonal be x cm.

$\: \: \: \: \: Area \: \: of \: \: Rhombus \: \: \frac{1}{2} \: \times {d_1} \: \times \: {d_2}$

$\: \: \: \: \: \leadsto \: \: {10} \: \: = \: \: \frac{1}{\cancel{2}} \: \times \cancel{4} \: \times \: {x}$

$\: \: \: \: \: \leadsto \: \: {10} \: \: = \: \: {2} \: \times \: {x}$

$\: \: \: \: \: \leadsto \: \: {10} \: \: = \: \: {2x}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{10}{2}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {5} \: cm$

Hence, the length of the other diagonal of the rhombus is 30cm.

$\large\underline\pink{Property \: \: Of \: \: Rhombus:-}$

1. A rhombus all side are equal.
2. A rhombus opposite angle are equal.
3. A rhombus the sum of adjacent angle angle supplementary i.e. (<A + <D = 180°).
4. A rhombus, each diagonal of a rhombus divides it into two congruent triangle.
5. A rhombus, if one angle is right, then all angle are right.
6. Diagonal of a rhombus bisect each other and also perpendicular to each other.

$\large\underline\pink{More \: \: Important :-}$

• Area of rhombus = b × h
• Perimeter of rhombus = 4 × side

where,

• b = base
• h = height
• p = perimeter
• a = area