Question

The perimeter of a rhombus is 160 cm and one of its diagonal has a length of 40 cm. Find the area of the rhombus. 1a​

Answer 1

Answer:

Step-by-step explanation:

Taking square root on both side

Area=1/2*40*30

=600 sq.cm

Answer 2

Solution:

Let the one diagonal be a and other diagonal be b.

Perimeter of rhombus = 160cm

Length of one diagonal = 40cm

Length of other diagonal = ?

Area of rhombus = ?

Calculating Length of other Diagonal(b)

$\boxed{\large \: P = 2 \sqrt{(a)^2 + (b)^2}}$

$\implies{160 = 2 \sqrt{(40)^2 + (b)^2} }$

$\implies{2 \sqrt{{40}^{2} + b^2} =160}$

Dividing both sides by 2

$\implies{ \frac{2 \sqrt{40^2 + b^2} }{2} =\cancel\frac{160}{2} }$

$\implies{ \sqrt{40^2 + b} = 80}$

Squaring both sides

$\implies{b=40 \sqrt{3}}$

$\implies \boxed{b = 70}$

Therefore, length of other side is 70cm

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Calculating Area of Rhombus

$\boxed{ Area \: of \: Rhombus \: =\frac{1}{2}×a×b}$

$= \frac{1}{2} \times 40 \times 70$

$= 20 \times 70$

$= \boxed{1400cm^{2}}$

Hence,

Area of rhombus is $\large{\underline{\frak{1400cm^2}}}$

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