Waist-to-hip ratio. Dr. Aaron R. Folsom, from the University of Minnesota School

Question

Waist-to-hip ratio. Dr. Aaron R. Folsom, from the University of Minnesota School of Public Health, has concluded that for a man aged 50 to 69 to be in good health, his waist size w should be less than or equal to 95% of his hip size h as shown in the figure.

a)

Write an inequality that describes the region shown in the figure.

b)

Is a man in this group with a 36-inch waist and 37-inch hips in good health?

c)

If a man in this group has a waist of 38 inches, then what is his minimum hip size for good health?

a)

Write an inequality that describes the region shown in the figure.

b)

Is a man in this group with a 36-inch waist and 37-inch hips in good health?

c)

If a man in this group has a waist of 38 inches, then what is his minimum hip size for good health?

Explanation / Answer

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We have been given the fact that waist size w should be less than or equal to 95% of his hip size h

a. So,In equality that describes the region is :

y<=0.95(x)+30/.95

y<= .95x + 31.6

b. With a 36inch waist and 37inch hip will have a hip size ratio of 36/37 = .973 which is more than the permitted

value for good health of .95. Hence, a man with 36inch waist and 37 inch hips is not in good health.

c. If a man has waist of 38-inch then .95 <= w/h

or

38/h >= .95

h >= 38/.95 = 40

So, minimum hips should be 40 inches

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