Question

the area of rohmbus is 210 cm square. if one of its diagonal is 14 cm then find its other diagonal​

Answer 1

Given

• Area of the Rhombus = 210cm².
• One diagonal = 14cm.

To Find

• Other diagonal.

Solution

Let the one diagonal be x and other diagonal be y.

Where,

• x = 14cm.
• y = ?

$\rm{Area \: of \: Rhombus = \frac{1}{2} \times x \times y} \\ \\ \\\rm\dashrightarrow \: \: \: \: \: \: \: {210 = \frac{1}{2} \times 14 \times y}\\ \\ \\\rm\dashrightarrow \: \: \: \: \: {7y = 210}\\ \\ \\\rm\dashrightarrow \: \: \: \: \:{y = \frac{210}{7}} \\ \\ \\\rm\dashrightarrow \: \: \: \: \: {y = 30cm.}$

Therefore, other diagonal = y = 30cm.

Verification

Let's find area using both diagonals.

Diagonal = x = 14cm.

Diagonal = y = 30cm.

Area of Rhombus = ½ × x × y.

⇢ Area of Rhombus = ½ × 14 × 30.

⇢ Area of Rhombus = 7 × 30

⇢ Area of Rhombus = 210cm².

We got area from both diagonals x and y, therefore our answer is correct.

Hence, verified.

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Answer 2

Given :-

• Area of a rhombus = 210 cm²
• Diagonal 1 = x = 14 cm

To Determine :-

• The value of diagonal 2 = y

We know that the formula for diagonal of a rhombus is :-

$\: \frac{1}{2} \times d_1 \times d_2$

Therefore, to determine the value of y we will put the values and equate L.H.S. and R.H.S.

$\rightarrow \: \frac{1}{2} \times 14 \times y = 210 {cm}^{2} \\ \rightarrow \: 7y = 210 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \rightarrow \:y = \frac{210}{7} = 30 \: {cm} \: \: \: \: \: \: \:$

Therefore the value of other diagonal is 30 cm