Question

Work out the length of ab​

Answer 1

AB= 2√137 cm

Explanation:

because we have a right triangle we apply the Pythagorean theorem

hypothenuse² = side² + side²

AB² = BC² + AC², substitute the given sides BC=8 and AC=22

AB² = 8² + 22² , square the numbers and apply the square root to both side

AB = √(64 + 484), add the numbers

AB = √548, simplify the square root

AB= 2√137 cm

Answer 2

AB = 2√137

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

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Trigonometry

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

• a is a leg
• b is another leg
• c is the hypotenuse

Explanation:

Step 1: Define

Identify variables

a = 22 cm

b = 8 cm

Step 2: Solve for c

1. Substitute in variables [Pythagorean Theorem]: (22 cm)² + (8 cm)² = c²
2. Evaluate exponents: 484 cm² + 64 cm² = c²
3. Add: 548 cm² = c²
4. [Equality Property] Square root both sides: 2√137 cm = c
5. Rewrite: AB = 2√137