Question

The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm. Then, the area of the rhombus in square centimeters​

Answer 1

We know in a rhombus each side is equal.

Let each side = X cm.

We have:

4X=100

X=100/4

X=25cm

Now let one of the diagonal be = Y cm and the other is 14 cm(Given)

See, this figure:

AB=25cm

AO=AC/2(Diagonalbisecteachother)

AO=14/2=7cm

BO=BD/2

BO=Y/2cm

IntriangleAOB

AngleAOB=90Degree(Diagonalsareperpendicular)

AO2+BO2=AB2(PythagorasTheorum)

72+(Y/2)2=252

49+(Y2)/4=625

(Y2)/4=625–49=576

Y2=576∗4

Y=24∗2

Y=48cm

Y/2=24cm

Now we know area of Rhombus = 4*(Area of triangle AOB)

AreaofTriangleAOB=(1/2)∗AO∗BO

=(1/2)∗24∗7

=12∗7

=84sq.cm

AreaofRhombus=4∗84

=336sq.cm

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