Question

a formula is used in the medical field to estimate a persons body surface area. the formula is $a = \frac{\sqrt{hw}}{60}$, where a is body surface area in square meters, h is height in centimeters, and w is weight in kilograms.
a. compute the body surface area of a person who is 182 cm tall and weighs 92.9 kg.
b. if a woman is 164 cm tall and has body surface area of 1.74 $m^2$, how much does she weigh?
a. $a \approx \square$ square meters
(round the final answer to the nearest hundredth as needed. round all intermediate values to the nearest hundredth as needed.)

Explanation:

Step1: Substitute h=182, w=92.9 into formula

$A = \frac{\sqrt{182 \times 92.9}}{60}$

Step2: Calculate product inside square root

$182 \times 92.9 = 16907.8$

Step3: Compute square root of the product

$\sqrt{16907.8} \approx 130.03$

Step4: Divide by 60 to find A

$A \approx \frac{130.03}{60} \approx 2.17$

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Step1: Rearrange formula to solve for w

Starting with $A = \frac{\sqrt{hw}}{60}$, multiply both sides by 60: $60A = \sqrt{hw}$. Square both sides: $(60A)^2 = hw$, so $w = \frac{(60A)^2}{h}$

Step2: Substitute A=1.74, h=164

$w = \frac{(60 \times 1.74)^2}{164}$

Step3: Calculate 60×1.74

$60 \times 1.74 = 104.4$

Step4: Square the result

$104.4^2 = 10899.36$

Step5: Divide by 164 to find w

$w \approx \frac{10899.36}{164} \approx 66.46$

Answer:

a. $A \approx 2.17$ square meters
b. $w \approx 66.46$ kilograms