Question

the area of a rhombus is
80 {m}^{2}80m2
and one diagonal is 24m
then find the other diagonal​

Answer 1

Given: The area of the rhombus is 80m² and the diagonal is 24m

To Find: the other diagonal of the rhombus

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We, know here the given measures are the area and the diagonal of the rhombus so, let's use this Required formula which is as follow

$\star\blue{ \underline{ \boxed{ \pink{ \mathfrak{ area _{(rhombus)} = \frac{ d_{1} \times d_{2} }{2} }}}}}$

Where, d₁ stands for the first diagonal of the rhombus and d₂ stands for the second diagonal of the rhombus .So, now the measure of the area is 80m² and the diagonal 1 measures 24m Now, by using the above formula let's find the values.

by , using the Required formula and substituting the values we get the following equation :

${ : \implies} \sf 80m = \frac{24 \times d_{2}}{2} \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: 24 \times d_{2} = 80 \times 2 \\ \\ \\ \\ { : \implies} \sf \: 160 = 24 \times d_{2} \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: d_{2} = \cancel\frac{160}{24} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf d_{2} = { \pink{ \underline{ \boxed{ \pmb{\frak{6.6m}}}}}} \: \: \: \: \: \: \: \: \: \: \:$

${ \underline{ \rm{hence \: the \: second \: diagonal = \pmb{6.66m}}}}$

Answer 2

Given :-

• Area of Rhombus = 80m²
• One Diagonal of Rhombus = 24m

To Find :-

• Second Diagonal of the Rhombus

Solution :-

❏ As we know that, Area of Rhombus is given by [ Area of Rhombus = ½ × products of Diagonal ] or we can say that [ Area of Rhombus = ½ × ( D1 × D2 ].

Putting the Values :

➞ Area of Rhombus = ½ × ( D1 × D2 )

➞ 80 = ½ × ( 24 × D2 )

➞ 80 × 2 = ( 24 × D2 )

➞ 160 = ( 24 × D2 )

➞ 160 / 24 = Diagonal 2

➞ 6.6m = Diagonal 2

Thus Second Diagonal of the Rhombus is 6.6m

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★ Additional Info :

Formulas Related to Area :

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

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