Question

Which of the following shows the length of the third side, in inches, of the triangle below?

Answer 1

20 inches

Explanation:

Step 1: Understanding Pythagorean Theorem

The Pythagorean Theorem is
`a^(2) +b^(2)+c^(2)`. It is used to find the side lengths of a right triangle.

Step 2: Using the Theorem

We can see that the triangle shown is a right triangle and we know two sides so we can solve for the last side.

We can denote -

a - 15

b - unknown

c - 25

(note, c is always the hypotenuse or the longest side of the triangle)

We can plug in the numbers -

`15^(2) +b^(2) =c^(2)`

`225 +b^(2)=625`

`b^(2) =625-225`

`b^(2) =400`

`b=20`

Answer 2

20 inches

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Trigonometry

• [Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Explanation:

Step 1: Identify Variables

Leg a = x

Leg b = 15

Hypotenuse c = 25

Step 2: Solve for x

1. Substitute [PT]: x² + 15² = 25²
2. Isolate x term: x² = 25² - 15²
3. Exponents: x² = 625 - 225
4. Subtract: x² = 400
5. Isolate x: x = 20