Question

(i) The length of the diagonals of a rhombus are 16 cm. and 12 cm. respectively. Find the length of its sides . ( ii ) The ratio of two sides of a parallelogram is 4 : 3 . If the perimeter is 56 cm. , Find the lengths of its sides .​

Answer 1

Answer:

Diagonals of rhombus are cut each other at 90o.

Since d1=16and d2=12

Therefore, by Pythagoras theorem 

 a2=(2d1)2+(2d2)2

⇒ a2=82+62 

⇒  a=100=10



Step-by-step explanation:

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Answer 2

Question 1 :

The length of the diagonals of a rhombus are 16 cm. and 12 cm. respectively. Find the length of its sides .

Solution :

Let ABCD be rhombus with AC and BD diagonals and AC and BD bisect at O.

Therefore,

AO = 16/2=8 cm

BO = 12/2=6cm

In right angled triangle AOB, by Pythagoras theorem

AB^2=AO^2+OB^2

AB^2=82+62

AB^2= 64 + 36

AB= √ 100

AB =10

Length of rhombus is 10 cm

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Question 2 :

The ratio of two sides of a parallelogram is 4 : 3 . If the perimeter is 56 cm. , Find the lengths of its sides .

Solution :

Let the sides of a parallelogram be 4x and 3x.

We know that,

Opposite sides of a parallelogram are equal in length.

Perimeter = 2(4x) + 2(3x)

→ 56 = 14x

→ x = 4

Therefore the length of the sides of a parallelogram are

• 4x = 4(4) = 16 cm
• 3x=3(4) = 12 cm.