Question

The sides of a rhoumbus are 25cm long ,if the diagonal is 30cm long then whats is the lenght of the other diagonal?

Answer 1

Given:

The sides of a rhoumbus are 25cm long.

The diagonal is 30cm long.

Required:

To find the length of the other diagonal.

Step-by-step explanation:

Interior of a rhombus is made up of four congruent right triangles and diagonals of rhombus are perpendicular bisectors of each other. So in all those right triangles, half length of diagonals act as legs and sides act as hypotenuse.

Now the one diagonal is 30 cm.

From Pythagoras theorem,

`\begin{gathered} 15^2+x^2=25^2 \\ \\ 225+x^2=625 \\ \\ x^2=625-225 \\ \\ x^2=400 \\ \\ x=20cm \end{gathered}`

Now the length of other diagonal is

`\begin{gathered} =20+20 \\ =40cm \end{gathered}`

Final Answer:

The length of the other diagonal is 40 cm.