Question

The length of the diagonals of a rhombus is 42 cm and 40 cm. Find the perimeter of the rhombus.

Answer 1

Answer:

Solve for perimeter

P=116cm

p Diagonal

42

cm

q Diagonal

40

cm

Using the formulas

P=4a

a=p2+q2

2

Solving forP

P=2p2+q2=2·422+402=116cm

Answer 2

$\huge\sf\pink{Answer}$

☞ Perimeter if the Rhombus is 116

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$\huge\sf\blue{Given}$

✭ Length of the Diagonals are 42 cm & 40 cm

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$\huge\sf\gray{To \:Find}$

◈ The perimeter of the Rhombus?

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$\huge\sf\purple{Steps}$

We know that the side of a Rhombus is given by,

$\underline{\boxed{\sf a= \sqrt{(\dfrac{d_2}{2})^2+ (\dfrac{d_1}{2})^2}}}$

Substituting the given values,

➳ $\sf a= \sqrt{(\dfrac{d_2}{2})^2+ (\dfrac{d_1}{2})^2}$

➳ $\sf a = \sqrt{(\dfrac{42}{2})^2 + (\dfrac{40}{2})^2}$

➳ $\sf a = \sqrt{(21)^2+(20)^2}$

➳ $\sf a = \sqrt{441+400}$

➳ $\sf a = \sqrt{841}$

➳ $\sf \red{a = 29}$

Perimeter of a Rhombus is given by,

$\underline{\boxed{\sf Perimeter = 4a}}$

Substituting the values,

➝ $\sf Perimeter = 4a$

➝ $\sf Perimeter = 4\times 29$

➝ $\sf \orange{Perimeter = 116 \ cm}$

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