Problem 53 - Algebra 1

Question

Physicians can approximate the Body Surface Area of an adult (in square meters) using an index called \(B S A\) where \(H\) is height in centimeters and \(W\) is weight in kilograms. Body Surface Area: \(\sqrt{\frac{H W}{3600}}\) Find the \(B S A\) of a person who is 180 centimeters tall and weighs 75 kilograms.

Step-by-Step Solution

Answer

The BSA (Body Surface Area) of a person who is 180 centimeters tall and weighs 75 kilograms is approximately 1.94 square meters.

Step 1: Identify the Given Values

The height (\(H\)) of the person is given as 180 centimeters and the weight (\(W\)) of the person is given as 75 kilograms.

Step 2: Substitute the Values into the Formula

Substitute the given values of \(H = 180\) cm and \(W = 75\) kg into the formula for the Body Surface Area. This gives \(BSA = \sqrt{\frac{H W}{3600}} = \sqrt{\frac{180 \cdot 75}{3600}}\).

Step 3: Compute the Value of the Numerator

Compute the value of the numerator in the square root, which is the product of \(H\) and \(W\), which equals \(180 \cdot 75 = 13500\).

Step 4: Compute the Value Inside the Square Root

Compute the value inside the square root, which is the result of dividing 13500 by 3600. This equals \( \frac{13500}{3600} ≈ 3.75 \).

Step 5: Compute the Final Value of BSA

Compute the final value by taking the square root of 3.75. Which equals approximately 1.94 square meters.

Key Concepts

mathematical formulas

When determining the Body Surface Area (BSA) of an individual, we utilize a specific formula that involves both height and weight. This is expressed in the equation for BSA: \( BSA = \sqrt{\frac{HW}{3600}} \). This formula is significant because it requires us to find the surface area of the body in square meters, which can provide useful health-related insights. The equation showcases the relationship between the height (\(H\)) in centimeters, the weight (\(W\)) in kilograms, and a constant number, 3600, which helps scale the height and weight in terms of body surface area. Throughout the application of any mathematical formula, it’s crucial to understand the components involved and how each variable interacts. This comprehension is essential to ensure accurate problem-solving and calculation.

problem solving

Approaching a problem like calculating BSA involves several methodical steps, ensuring you work logically towards the solution. Begin by identifying the values given in the problem. Here, you are provided with a height of 180 cm and a weight of 75 kg. Plugging these values into the formula creates an expression: \( \sqrt{\frac{180 \times 75}{3600}} \). This structured problem-solving approach helps manage complex tasks by dividing them into simpler, more manageable steps.

• Identify the known variables.
• Substitute these values into the given formula.
• Proceed step by step to simplify and solve the expression.

Breaking down your problem into stages helps verify each part of the computation, thereby minimizing errors and enhancing the learning process.

square root calculation

Calculating the square root is a fundamental math skill, especially when dealing with formulas like the BSA calculation. After obtaining the expression \( \sqrt{\frac{13500}{3600}} = \sqrt{3.75} \), your task is to find the square root of 3.75. To compute the square root:

• Consider rounding for simplicity, without losing significant accuracy. Here, the square root of 3.75 equates approximately to 1.94.
• Use a calculator or square root chart if necessary to avoid errors in manual estimation.

Understanding how to accurately calculate or estimate the square root helps in verifying computations and ensuring precision in real-world applications. By perfecting this skill, you also foster a more profound understanding of how it interacts within larger mathematical formulas and expressions.