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A rhombus has sides of length 10 cm and one diagonal of length 12 cm. How long is the other diagonal, in cm?

Respuesta :

mhanifa

Answer:

16 cm

Step-by-step explanation:

Side of the rhombus and half diagonals form a right triangle

We have hypotenuse= 10 cm and one leg= 12/2= 6 cm

The other leg:

  • d/2= √10²-6²= √64= 8 cm

So the other diagonal is twice as 8 cm leg, d= 8 cm * 2=  16 cm

The length of the other diagonal is 16cm

  • First and foremost, it should be noted that the length of the rhombus and the half diagonals will form a right angle. Therefore, 12cm will be divided by 2 which is 6cm.

Then, we'll use Pythagoras theorem which will be:

a² + b² = c²

6² + b² = 10²

36 + b² = 100

Collect like terms

b² = 100 - 36

b² = 64.

b =✓64.

b = 8cm

Then, the diagonal will be twice of b

= 2b = 2 × 8 = 16cm

Therefore, the other diagonal is 16cm.

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