Question

Perimeter of a rhombus is 100cm, its one of the diagonal is 40cm. Find another diagonal.​

Answer 1

Answer:

30cm

Step-by-step explanation:

Perimeter of the rhombus = 100 cm

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

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 = 20 cm

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

By applying pythagoras 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.

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