Question

The perimeter of a rhombus is 100 cm.One of its diagonal is 40cm .Find the length of the other diagonal .

Answer 1

Here is your answer buddy,

$\textbf{GIVEN}$

Perimeter of the rhombus = 100 cm

Now, Let, ABCD be the rhombus and AC and BD be the diagonals.

$\textbf{Therefore}$

We know that,

Perimeter of the rhombus = 4× side

So,
100 = 4×side
=> side = 25

Now, Given diagonal = 40cm

Let, BD = 40 cm

Now rhombus has one property that its diagonals bisect each other at right angles.

Therefore, AO = OC and OB = OD = 20cm

Hence angle AOB = angle BOC = angle COD = angle AOD = 90 (making each triangle a right triangle)

By applying pythagorus theorem in triangle AOB we get OB = 20cm and AB = 25 cm and angle O is 90

$AB^{2}$ = $OB^{2} + AO^{2}$
=> $25^{2}$ = $20^{2} + AO^{2}$
=> $25^{2} - 20^{2}$ = $AO^{2}$
=> 625 - 400 = $AO^{2}$
=> 225 = $AO^{2}$
=> $15^{2}$ = $AO^{2}$
=> AO = 15 cm.

Now the diagonal is AC = (AO + OC) = 30 cm.

The diagonals are AC = 30 cm and BD = 40 cm.

Hope this helps you.
Be Brainly.

Answer 2

Answer:

Answer is 30cm

I hope this answer helps you

All the best