Question

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Answer 1

Step-by-step explanation:

area of rhombus =

$\frac{1}{2} (d1 \times d2) = 50 \sqrt{3} \\ = \frac{1}{2} \times 1 0 \times d2 = 50 \sqrt{3} \\ d2 =( 2 \times 50 \sqrt{3}) \div 10 \\ = 2 \times 5 \sqrt{3} = 10 \sqrt{3}$

other diagonal is 10√3 units

In a rhombus, diagonals bisect each other at right angles.

The two diagonals of a rhombus form four right-angled triangles which are congruent to each other

since diagonals are bisect each other at O. we have AO = OC = 5√3

BO = OD = 5

since ∆ AOB forms right angled triangle by Pythagoras theorem we have

AO² + BO² = AB²

${(5 \sqrt{3})}^{2} + {5}^{2} = 25 \times 3 + 25 = 75 + 25 = 100$

then AB² = 100

AB = √100 = 10 units.

length of the side of the rhombus = 10 units.

perimeter = 4(side) = 4(10) = 40 units