Use the equation to find the length of the missing leg measure.
[tex]a^2+16^2=20^2[/tex]
1. Evaluate powers: [tex]a^2+256=400[/tex]
2. Undo addition: [tex]a^2=144[/tex]
3. Undo the square: [tex]a=\sqrt{144}[/tex]
What is the length of the missing leg measure?
[tex]a=[/tex] $\square$ units
Answer (1)
The problem provides the equation a 2 + 1 6 2 = 2 0 2 and the steps to solve for a .
Simplify the equation to isolate a : a = 144 .
Calculate the square root of 144: a = 12 .
State the final answer: 12
Explanation
Understanding the Problem We are given the equation a 2 + 1 6 2 = 2 0 2 and the steps to solve for a . Our goal is to find the value of a , which represents the length of the missing leg measure.
Isolating the Variable The equation is already simplified to a = 144 . To find the value of a , we need to calculate the square root of 144.
Calculating the Square Root The square root of 144 is 12, since 12 × 12 = 144 . Therefore, a = 12 .
Stating the Answer The length of the missing leg measure is 12 units.
Examples
The Pythagorean theorem, which is the basis for this problem, is used in construction to ensure that corners are square (90 degrees). For example, if you're building a rectangular foundation, you can use the 3-4-5 rule (a multiple of the Pythagorean theorem) to make sure the corners are right angles. If two sides of a triangle are 3 feet and 4 feet, the hypotenuse must be 5 feet for the triangle to be a right triangle. This principle helps in creating stable and accurate structures.
