Question

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of a rhombus is (a) 8 cm (b) 9 cm (c) 10 cm (d) 12 cm

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Side\:of\:rhombus=10\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Diagonal( D_{1}) = 16 \: cm \\ \\ \tt: \implies Diagonal( D_{2}) = 12 \: cm \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Side \: of \: rhombus = ?$

• According to given question :

$\tt \circ \: OA = 8 \: cm \\ \\ \tt \circ \: OB = 6 \: cm \\ \\ \bold{In \: right \: angled \: \triangle \: AOB} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \: \: \: \: \: \: (phythagoras \: theorem) \\ \\ \tt: \implies {AB}^{2} = {OA}^{2} + {OB}^{2} \\ \\ \tt: \implies {AB}^{2} = {8}^{2} + {6}^{2} \\ \\ \tt: \implies {AB}^{2} =64 + 36 \\ \\ \tt: \implies {AB}^{2} =100 \\ \\ \tt: \implies {AB} = \sqrt{100} \\ \\ \green{\tt: \implies {AB} =10 \: cm} \\ \\ \green{\tt \therefore Side \: of \: rhombus \: is \: 10 \: cm}$

Answer 2

Answer:

(c) 10 cm

Step-by-step explanation:

Length of the diagonals of the given rhombus are 16cm and 12cm

According to question:-

We will use Pythagoras theorem here.

(P)^2 + (B)^2 = (H)^2

(8)^2 + (6)^2 = (H)^2

64 + 36 = (H)^2

100 = (H)^2

√100 = H

10cm = H

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