Question

The side of a rhombus is 10 cm. The smaller diagonal is 1/3 of the greater diagonal. Find the length of the greater diagonal. [give proper explanation]

Answer 1

Answer:

Step-by-step explanation:

Rhombus ABCD, AB= 10cm , So BC = 10cm , as all sides of rhombus are equal.

Diagonal AC = 12cm

So, area( tri ABC) by Heron's formula

= √{ s(s-a)(s-b)(s-c) } , s is semi perimeter & a,b,c are sides of the triangle

= s = 32/2 = 16

Area = √{16 *(16–10)(16–10)(16–12)

=> area = √(16*6*6*4)

=> area = √(2²*2²*2²*3²*2²)

=> area = 2*2*2*3*2 = 48 cm²

=> area (Rhombus ABCD) = 48*2 = 96 cm²

MARK IT THE BRAINLIEST

Answer 2

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the diagonals are AC and BD where BD>AC...

let,AO=OC=x

∴OB=√(10²-x²)=OD ❪as,diagonals of a rhombus bisect each other at right angles❫

now..BD=OB+OD=2√(10²-x²)

now...AC=AO+OC=2x

now.. according th the problem...

➤2√(10²-x²)=3×(2x)

➤√(10²-x²)=3x

➤(10²-x²)=9x²

➤10x²=100

➤X=√10

therefore...AC=2√10cm

and BD=2√(100-10)=2√90=6√10 cm

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