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Question

If the diagonal of the given square is 4 cm, find its perimeter and area.


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Solution

Angles of the triangle ABC are 45,45,90

sin(45):sin(45):sin(90)

12:12:1

1:1:2

So, the sides AB,BC & AC will be in the ratio 1:1:2

Hence AB:BC:AC1:1:2

The ratio will be x:x:2x

Since AC =4, So 2x=4

x=22

So, the ratio AB:BC:AC will be equal to 22:22:4

which gives AB=22cm

BC=22cm

AC =4 cm

Area =AB×BC=22×22=8cm2

Perimeter =4(AB)=4×22=82cm


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