Question

the length of diagonals of a rhombus are 48cm and 14cm.the perimeter of the rhombus is​

Answer 1

★ Solution :-

In the question we are given with the measurements of the two diagonals of a Rhombus. We are asked to find the perimeter of the Rhombus. So, first we should find the measurement of each side of the Rhombus.

We can find the side of the Rhombus by Pythagoras theorem.

Side of the Rhombus :-

$\sf \leadsto {Hypotnous}^{2} = {Base}^{2} + {Perpendicular}^{2}$

$\sf \leadsto {LM}^{2} = {MO}^{2} + {LO}^{2}$

$\sf \leadsto {LM}^{2} = {7}^{2} + {24}^{2}$

$\sf \leadsto {LM}^{2} = 49 + 576$

$\sf \leadsto {LM}^{2} = 625$

$\sf \leadsto \sqrt{{LM}^{2}} = \sqrt{625}$

$\sf \leadsto LM = \sqrt{625}$

$\sf \leadsto LM = 25 \: cm$

Now, we know that all the sides in a Rhombus measures same. So,

Perimeter of the Rhombus :

$\sf \leadsto Perimetre_{(Rhombus)} = 4 \times side$

$\sf \leadsto Perimetre_{(Rhombus)} = 4 \times 25$

$\sf \leadsto Perimetre_{(Rhombus)} = 100 \: cm$

Therefore, the perimeter of the Rhombus is 100 cm.

Answer 2

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