Question

The perimeter of a rhombus is 4m. One of its diagonal is 4/3rd of the other.
Find the area of the rhombus.
1) 84m2
2) 108m² 3) 144m²
4) 96m​

Answer 1

Answer:

ANSWER

Perimeter of rhombus =4×side

⇒  100=4×side

⇒  side=4100

⇒  side=25

We know diagonals of a rhombus divides the rhombus in two equilateral triangle.

Now, we are going to find area of 1 equilateral triangle.

Semi perimeter =225+25+40=45

We will use Heron's formula to find are of equilateral triangle.

⇒  Area of triangle =s(s−a)(s−b)(s−c)

                                 =45(45−40)(45−25)(45−25)

                                 =45×5×20×20

                                 =90000

                                 =300m2

⇒  Area of rhombus =2×300m2=600m2

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Perimeter of rhombus=100 cm

∴one side of rhombus=

4

100

=25cm

Since diagonal of a rhombus bisect each other at right angle

∴AO=

2

1

×14=7cm.and∠AOB=90

∘

In ΔAOB

OB=

AB

2

−AO

2

OB=

25

2

−7

2

OB=

625−49

OB=

576

OB=24cm

∴ Length of other diagonal=2×OB=2×24=48cm

Area of the rhombus =

2

1

×product of diagonal

⇒

2

1

×48×14=336sq.cm