Question

A rhombus and a triangle are equal in areas. if the base and height of the triangle are 24.8 cm and 5.5 cm respectively and the length of one diagonal of the rhombus is 22 cm, find the length of other diagonal of the rhombus.​

Answer 1

Given :

• Area of Rhombus and Triangle are equal .
• Base and Height of Triangle is 24.8 cm and 5.5 cm respectively .
• Length of one diagonal of rhombus is 22 cm .

To Find :

• Length of other diagonal of the rhombus.

Solution :

Firatly we will find Area of Triangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:\triangle=\dfrac{1}{2}\times{b}\times{h}}$

Putting Values :

$\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{{\cancel{24.8}}}\times{5.5}}$

$\longmapsto\tt{12.4\times{5.5}}$

$\longmapsto\tt\bf{68.2\:{cm}^{2}}$

Now ,

As Given that Area of Rhombus and Triangle are equal . So ,

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rhombus=\dfrac{1}{2}\times{{d}_{1}}\times{{d}_{2}}}$

Putting Values :

$\longmapsto\tt{68.2=\dfrac{1}{{\cancel{2}}}\times{{\cancel{22}}}\times{{d}_{2}}}$

$\longmapsto\tt{68.2=11\times{{d}_{2}}}$

$\longmapsto\tt{{d}_{2}=\cancel\dfrac{68.2}{11}}$

$\longmapsto\tt\bf{{d}_{2}=6.2\:cm}$

So , The Length of other Diagonal of Rhombus is 6.2 cm .

Answer 2

Answer:

Given :-

• Area of Rhombus = Area of Triangle
• Base and Height of Triangle is 24.8 cm and 5.5 cm respectively .
• Length of one diagonal of the rhombus is 22 cm .

To Find :-

Length of other Diagonal

Solution :-

As we know that

Area of triangle = ½ × Base × Height

Area = ½ × 24.8 × 5.5

Area = 1 × 12.4 × 5.5

Area = 12.4 × 5.5

Area = 68.2 cm²

Now,

Area of rhombus = ½ × D1 × D2

68.2 = ½ × 22 × D2

68.2 × 2 = 22 × D2

136.4 = 22 × D2

136.4/22 = D2

6.2 = D2

Hence :-

Other Diagonal is 6.2 cm.