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  • Write True or False and justify your answer: If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm^{2}.

Write True or False and justify your answer:

If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm^{2}.

Answers (1)

Solution

Side\; of\; rhombus = 10 cm

One\; Diagonal = 16 cm

We know that diagonals of rhombus interest each other at a right angle

So\; In\; right\; \Delta AOB

Using\; Pythagoras\; theorem

(AB)^{2} = (OA)^{2} + (OB)^{2}

(10)^{2} = (8)^{2} + (OB)^{2}

100 = 64 + (OB)^{2}

100 -64=\left ( OB \right )^{2}

(OB)^{2} = 36

OB=\sqrt{36} \; \; \; \; \; \; \; \left [ Q\sqrt{36}=\sqrt{6\times 6}=6 \right ]

OB = 6 cm

\therefore BD = 2\; \times \; OB

BD = 2 \times 6 = 12 cm

Now, Area\; of\; rhombus = \frac{1}{2}\; \times product\; of \; its\; diagonals

= \frac{1}{2} \times BD \times AC

=\frac{1}{2} \times 12 \times 16

= 6 \times 16 = 96 cm^{2}

Hence, the area of a rhombus is 96 cm^{2}

Therefore the given statement is true.

 

Posted by

infoexpert21

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