Question

The ratio of the lengths of an ellipse is 3:2. If it’s area is 150 cm2, what are the lengths of The major and minor semiaxes respectively?

Answer 1

Major: 8.5 cm

Minor: 5.6 cm

Explanation:

Answer 2

the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.

Explanation:

Area of ellipse = π*a*b

Let major semiaxes = a and minor semiaxes = b

then a:b = 3:2

a/b = 3/2

=> a = 3/2 b

Putting in the value of formula

150 = π * (3/2)b * b

150 = 3.14 * 1.5b * b

150= 4.71 b^2

150/4.71 = b^2

=> b^2 = 31.8

b= 5.63

a = 3/2 * b

a = 1.5 * 5.63

a = 8.45

So, the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.