Question

area of a rhombus is 182 sq.cm . if the length of its one diagonal is 13cm, then the length of its other diagonal ​

Answer 1

Answer :

(in the attachment)

Steps followed :

1. To answer such questions we need to be clear with the formula : Area of Rhombus : ½( d¹ × d²)
2. Now as we have known the formula we will consider the unknown value of the second diagonal as x .
3. Substituting the values in the equation we get : ½(13 × x ) = 182
4. We can divide 2 with 13 to get 6.5
5. 6.5 multiplied with x gives 6.5x
6. When we divide 182 by 6.5 to find x we get the value of x as 28 which means that the value of second diagonal is 28 .
7. Now to verify we need to put 28 in place of x and check if we get 182 as output and we got thr same . So the answer is correct .

Second diagonal : 28cm

Answer 2

Given:

• Area of rhombus = 182 sq cm
• One diagonal = d1 = 13cm

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Need to find:

• Other diagonal = d2=?

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Solution:

Area of a rhombus = $\frac{1}{2} d1 \times d2$

Now substituting values we get,

$\implies \: 182 = \frac{1}{2} \times 13 \times d2$

$\implies \: d2 = (182 \times 2) \div 13 cm$

$\red{\large{\bold{\boxed{ \implies \: d2 = 28 cm}}}}$

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Knowledge cell:

• A rhombus is a parallelogram

• All the sides of a rhombus are equal in length

• The diagonals of a rhombus make 90° with each other

• Perimeter of rhombus = 4 × measure of each side

• Number of edges = 4

• Number of vertices = 4