Question

The lengths of the diagonals of a rhombus are 12 and 16. What is the length of a side of a rhombus.

Answer 1

Answer:

10cm

Step-by-step explanation:

the length of the diagonal is 12cm and 16cm respectively.

half of the length of the diagonal would be 6cm and 8cm respectively.

the diagonals bisect at right angles.

We can use pythagoras theorem to find the length of one side.

a2 + b2 = c2

(8)2 + (6)2 = c2

64 + 36 = c2

100 = c2

10= c

therefore the length of the side of a rhombus is 10cm.

Hope this helps:)

Answer 2

Answer:

DC = BC = AB = AD = 10

Step-by-step explanation:

According to the property of rhombus

• Diagonals of rhombus bisect each other in equal ratio

which mean AE = EC

& DE = EB

Now consider, AC =16 and BD = 12

By the property of rhombus

AC = 2AE =2EC

AE = EC = AC =8

2

Similarly,

DE = EB = BD = 6

2

Magnitude of sides of rhombus are equal.

which means,

DC =CB = AB = AD

Consider a triangle ∆CEB

angle CEB = 90° [By the property of diagonal]

So we can apply Pythagoras law

according to which

(EC)^2 + (EB)^2 = (CB)^2

(8)^2 + (6)^2 =(CB)^2

64 + 36 = (CB)^2

100 = (CB)^2

√100= CB

CB = 10

As we know magnitude of the side of rhombus are equal .

CB = DC=AB =AD = 10

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