Determine whether the given lengths can be side lengths of right triangle. 1. 15, 36, 39 2. 3, 7, 10 3. 8, 15, 17 4. root3, root4, root5 5. 6, 7, 8, 6. 12, 16, 20

Answers

1. YES

2. NO

3. YES

4. NO

5. NO

6. YES

Explanation

A right triangle has a property that it side length must meet. That is the pythagorean theorem.

It states that; For a right triangle ABC, c²=a²+b². Where a, b and c are the opposite side lengths to angle A,B and C respectively.

Q1

15, 36, 39

The longer side is our c.

39² = 36² + 15²

1521 = 1296 + 225

1521 = 1521

This is true. So the side lengths are for a right triangle.

Q2

3, 7, 10

The longer side is our c.

10² = 2² + 7²

100 = 4 + 49

100 = 53

This is not true. So the side lengths are NOT for a right triangle.

Q3

The longer side is our c.

8, 15, 17

17² = 8² + 15²

289 =64 + 225

289 = 289

This is true. So the side lengths are for a right triangle.

Q4

The long side is our c.

Root3, Root4, Root5

(√5)² = (√4)² + (√3)²

5 = 4 + 3

5 = 7

This is not true. So the side lengths are NOT for a right triangle.

Q5

The longer side is our c.

6, 7, 8,

8² = 6² + 7²

64 = 36 + 49

64 = 85

This is not true. So the side lengths NOT are for a right triangle.

Q6.

The longer side is always the c

12, 16, 20

20² = 12² + 16²

400 = 144 + 256

400 = 400

This is true. So the side lengths are for a right triangle.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.