Question

7. The area of a rhombus is 202.4 cm?. If one of its diagonals is 18.4 cm, find the length of the
other diagonal.
diagonals are 8 cm 8 mm and 6 cm 5 mm.​

Answer 1

Given :-

• Area of Rhombus = 202.4 cm²
• One Diagonal = 18.4 cm

To Find :-

• Length of the Other Diagonal .

Solution :-

${:} \longrightarrow \sf{\sf{Area \: of \: Rhombus \: = \: \dfrac{1}{2}\: \times \: Products \: of \: Diagonal }}$

${:} \longrightarrow \sf{\sf{202.4 \: = \: \dfrac{1}{\cancel 2}\: \times \: \cancel{18.4} \: \times \: Diagonal }}$

${:} \longrightarrow \sf{\sf{202.4 \: = \: 9.2 \: \times \: Diagonal }}$

${:} \longrightarrow \sf{\sf{\cancel\dfrac{202.4}{9.2} \: = \: Diagonal }}$

${:} \longrightarrow \sf{\bf{22 \: = \: Diagonal }}$

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Verification :-

${:} \longrightarrow \sf{\sf{Area \: of \: Rhombus \: = \: \dfrac{1}{2}\: \times \: Products \: of \: Diagonal }}$

${:} \longrightarrow \sf{\sf{202.4 \: = \: \dfrac{1}{2}\: \times \: 18.4 \: \times \: 22 }}$

${:} \longrightarrow \sf{\sf{ 202.4 \: = \: \dfrac{1}{2}\: \times \: 404.8 }}$

${:} \longrightarrow \sf{\sf{ 202.4 \: = \: \dfrac{1}{\cancel2}\: \times \: \cancel{404.8} }}$

${:} \longrightarrow \sf{\bf{ 202.4 \: = \: 202.4 }}$

Hence, Verified

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So, Other Diagonal is 22cm

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Formulas Related to Rhombus :-

• Side of Rhombus = 1/2 √(d1)² + (d2)²
• Perimeter = 4 × Side = 2√(d1)² + (d2)²
• Area = 1/2 × Products of Diagonal

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Answer 2

Answer:

Given, area of rhombus = 202.4 cm^2

One diagonal = 18.4 cm

Other diagonal = ?

Let the other diagonal be x

So, As we know;

Area of rhombus = 1/2 * (product of its diagonals)

202.4 cm^2 = 1/2 ( 18.4 * x )

202.4 = 9.2x

x = 202.4/9.2

x = 22 cm (diagonal)

Hence, the length of other diagonal is 22cm.

NOW LET'S CHECK THE VERIFICATION:

Area of Rhombus = 1/2 (product of its diagonals)

202.4 cm^2 = 1/2 (22*18.4)

202.4 = 1/2 * 404.8

202.4 = 404.8/2

202.4 = 202.4

LHS = RHS

Hence, Verified.

Length of the other diagonal is 22 cm.

HOPE IT HELPS UH☺