Question

a rectrangl with diagonal of length 20 cm has side in the ratio of 2:1.find the are of rectrangle​

Answer 1

Answer:

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Step-by-step explanation:

A rectangle with diagonals of length d=20cm has sides in the ratio 2+%3A+1.

diagonal divide a rectangle in two right-angle triangles

so, if sides of a rectangle are a and b then we can write equation

d%5E2=a%5E2%2Bb%5E2

since d=20cm, we have

%2820cm%29%5E2=a%5E2%2Bb%5E2

400cm%5E2=a%5E2%2Bb%5E2

since sides in the ratio 2+%3A+1, we have

a%3Ab=2+%3A+1 =>a=2b..substitute in eq. above

400cm%5E2=%282b%29%5E2%2Bb%5E2.......solve for b

400cm%5E2=4b%5E2%2Bb%5E2

400cm%5E2=5b%5E2

400cm%5E2%2F5=b%5E2

80cm%5E2=b%5E2

b=sqrt%2880cm%5E2%29

b=8.94cm

a=2b=>a=2%2A8.94cm=>a=17.88cm

Find the:

a) perimeter

P=2a%2B2b

P=2%2A17.88cm%2B2%2A8.94cm

P=2%2A17.88cm%2B2%2A8.944271909999159cm

P=35.76cm%2B17.88cm

P=53.64cm

b) area of the rectangle.

A=ab

A=17.88cm%2A8.94cm

A=159.8472cm%5E2