Question

What is the length of side 1

What is the length of side 2
What is the length of side 3
What is the perimeter of the triangle

Answer 1

Side 1: 5

Side 2: 4

Side 3:
`\bold{√(41)}`

Perimeter:
`\bold{9+√(41)}`

Explanation:

For side 1 and side 2, notice that it fits the grid spaces perfectly. For side 1, you can count 5 spaces. For side 2, you can count 4 spaces. For side 3, notice that the grid spaces aren't even. Some of them are cut through. We can use the Pythagorean Theorem.

Pythagorean Theorem:
`a^2+b^2=c^2`, there a and b are legs and c is hypotenuse.

`5^2+4^2=c^2` [simplify]

`25+16=c^2` [add]

`41=c^2` [square root both sides]

`c=√(41)`

Perimeter is finding the sum of all the sides together.

`5+4+√(41)` [simplify]

`9+√(41)`