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  • The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is (A) 9 cm (B) 10 cm (C) 8 cm (D) 20 cm

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

(A) 9 cm

(B) 10 cm

(C) 8 cm

(D) 20 cm

Answers (1)

Answer : [B]

Here ABCD is a rhombus and we know that the diagonals of a rhombus are perpendicular bisectors of each other.

Given: AC=16 \; cm and BD=12 \; cm

\Rightarrow AO=\frac{AC}{2}=\frac{16}{2}=8\; cm

also BO=\frac{BD}{2}=\frac{12}{2}=6\; cm and \angle AOB=90^{o}

Using Pythagoras theorem in \Delta AOB we get

AB^{2}=AO^{2}+OB^{2}

AB^{2}=8^{2}+6^{2}

AB^{2}=64+36

AB^{2}=100

AB=\sqrt{100}

AB=10\; cm

Hence option (B) is correct.

Posted by

infoexpert23

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