Question

The diagonals of a rhombus are 16 cm and 30 cm. Find the length of the side of the rhombus.​

Answer 1

Answer :- AB = BC = DC = AD = 17 cm.

Explanation :-

Let ABCD be the rhombus.

AC and BD are the diagonal of rhombus.

AC = 16 cm

BD = 30 cm

We known the diagonal of rhombus bisect each other at right angle

Therefore,

AO = 8 cm and OC = 8cm

DO = 15 cm and OB = 15 cm .

In triangle AOB,

Using Pythagoras theorem

$AB^{2}= AO^{2}+ OB^{2} \\ AB ^{2} = {8}^{2} + {15}^{2} \\ AB ^{2} = 64 + 225 \\ AB ^{2} = 289 \\ AB = \sqrt{289} \\ AB = 17 \: cm$

As we known all side of rhombus are equal

Therefore, AB = BC = DC = AD = 17 cm.

Answer 2

HeRe Is Your Ans ⤵

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Area = 1/2 × product of diagonals

so area = 1/2 × 30 ×16 = 240 cm²

also diagonals bisect each other at right angles

D2 = 1/2×30= 15cm

D1 = 1/2×16 = 8cm

therefore , by Pythagoras theorem,

15² + 8² = side²

√289 = side

side = 17 cm

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