Question

5. ABCD is a rhombus. The lengths of its diagonals AC and BD are 8 cm and
6 cm respectively. Find each side of the rhombus.​

Answer 1

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Answer 2

Answer:

Given ABCD is a rhombus. Hence, AB = BC= CD = DA.

Given, AC = 8 cm and BD = 6 cm.

Since, ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors. Hence, AE = EC = 4 cm and BE = ED = 3 cm.

Now, we know that,

AEB = BEC = CED = DEA = 90°

So, in the triangle AEB, AE= 4 cm, BE = 3 cm and AEB = 90°

By Pythagoreas Theorem,

AE^2 + BE^2= AB² = 42 + 32 = 16+ 9 = 25

AB^2 = 25

→ AB = 5 cm

Hence, the sides of the rhombus are of length 5 cm.

Step-by-step explanation:

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