Question

the perimeter of rhombus is 40 cm if one of the diagonal is 16 cm centimetre then find the length of other diagnal​

Answer 1

Answer:

12cm

Step-by-step explanation:

I expect that you understand

Answer 2

Answer:

Length of diagonal is 12 cm.

Step-by-step explanation:

Let the side of rhombus be x

$perimeter \: of \: rhombus \: = 40 \: cm \\ 4x = 40 \\ x = \frac{40}{4} \\ x = 10 \: cm$

We know that diagonals of rhombus bisect each other at right angle.

Considering a triangle ABC in which ( by pythagoras theorem)

${AB}^{2} = {BC}^{2} + {AC}^{2} \\ {BC}^{2} = {AB}^{2} - {AC}^{2} \\ {BC}^{2} = {10}^{2} - {8}^{2} \\ {BC}^{2} = 100 - 64 \\ {BC}^{2} = 36 \\ BC = \sqrt{36 } \\ BC = 6 \: cm$

So, the length of diagonal is = 2 × 6 = 12 cm

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