Question

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If the diagonals of a rhombus are 12 cm and 5 cm, find the perimeter of the rhombus.

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Answer 1

Given:

• the diagonals of a rhombus are 12 cm and 5 cm,

To Find:

• the perimeter of the rhombus = ?

Solution:

We know that,

∴ the side of rombhus = $\small{2 \sqrt{d_{1} ^{2} \times d_2 ^{2} }}$

$\space$

$: \longrightarrow \: \: \frac{1}{2} \sqrt{(12) ^{2} + (5) ^{2} }$

$\space$

$: \longrightarrow \: \: \frac{1}{2} \sqrt{144 + 52}$

$\space$

$: \longrightarrow \: \: \frac{1}{2} \sqrt{169}$

$\space$

$: \longrightarrow \: \: \frac{1}{2} \times 13$

$\space$

$: \longrightarrow \: \: \tt{\frac{13}{2} \: cm}$

$\space$

$: \longrightarrow \: \: \bf{ \red{6.5 \: \green{cm}}}$

$\space$

➝ The perimeter = 4 × side = 4 × 6.5 = 26 cm

Therefore, the perimeter = 26 cm.

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Answer 2

Let p = 12 and q = 5

Perimeter of rhombus = $2√p^2 + q^2$

Perimeter of the rhombus =$2√12^2 + 5^2$

=$2√144 + 25$

= $2√169$

= $2 × 13 = 26cm$

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