Question

A a right triangle has a hypotenuse length of 21 meters. It has

one leg with a length of 15 meters. What is the length of the other leg?
Express your answer as a square root.

Answer 1

√216 meters

Explanation:

» Concepts

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs is equal to the length of the hypotenuse squared. It's represented as an equation of a² + b² = c², where a & b are the legs, and c is the hypotenuse

» Application

To find the length of the other leg, we have to plug in the values of b and c into the equation. B would be 15 meters, and c would 21 meters.

» Solution

Step 1: Simplify both sides of the equation.

• 
  `a^2+15^2+21^2`
• 
  `a^2+225=441`

Step 2: Subtract 225 from both sides.

• 
  `a^2+225-225=441-225`
• 
  `a^2=216`

Step 3: Take square root of both sides.

• 
  `√(a^2) = √(216)`
• 
  `a = √(216)`

Therefore, the length of the other leg is √216 meters.